Homotopy and Hom Construction in the Category of Finite Hypergraphs

Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associat...
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Autor*in:	Zhang, Conglei [verfasserIn] Wang, Yanying Zhang, Zhiguo Dai, Wei

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Hom construction Homotopy of hypergraph Exponential hypergraph Hypergraph homomorphism Colorings of hypergraph Maximum simple hypergraph

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, 1985, 39(2023), 4 vom: 30. Juni
Übergeordnetes Werk:	volume:39 ; year:2023 ; number:4 ; day:30 ; month:06

Links:	Volltext

DOI / URN:	10.1007/s00373-023-02672-6

Katalog-ID:	SPR052103463

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520			\|a Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$.
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allfields	10.1007/s00373-023-02672-6 doi (DE-627)SPR052103463 (SPR)s00373-023-02672-6-e DE-627 ger DE-627 rakwb eng Zhang, Conglei verfasserin aut Homotopy and Hom Construction in the Category of Finite Hypergraphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. Hom construction (dpeaa)DE-He213 Homotopy of hypergraph (dpeaa)DE-He213 Exponential hypergraph (dpeaa)DE-He213 Hypergraph homomorphism (dpeaa)DE-He213 Colorings of hypergraph (dpeaa)DE-He213 Maximum simple hypergraph (dpeaa)DE-He213 Wang, Yanying (orcid)0000-0001-9079-290X aut Zhang, Zhiguo aut Dai, Wei aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 4 vom: 30. Juni (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:4 day:30 month:06 https://dx.doi.org/10.1007/s00373-023-02672-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 4 30 06
spelling	10.1007/s00373-023-02672-6 doi (DE-627)SPR052103463 (SPR)s00373-023-02672-6-e DE-627 ger DE-627 rakwb eng Zhang, Conglei verfasserin aut Homotopy and Hom Construction in the Category of Finite Hypergraphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. Hom construction (dpeaa)DE-He213 Homotopy of hypergraph (dpeaa)DE-He213 Exponential hypergraph (dpeaa)DE-He213 Hypergraph homomorphism (dpeaa)DE-He213 Colorings of hypergraph (dpeaa)DE-He213 Maximum simple hypergraph (dpeaa)DE-He213 Wang, Yanying (orcid)0000-0001-9079-290X aut Zhang, Zhiguo aut Dai, Wei aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 4 vom: 30. Juni (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:4 day:30 month:06 https://dx.doi.org/10.1007/s00373-023-02672-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 4 30 06
allfields_unstemmed	10.1007/s00373-023-02672-6 doi (DE-627)SPR052103463 (SPR)s00373-023-02672-6-e DE-627 ger DE-627 rakwb eng Zhang, Conglei verfasserin aut Homotopy and Hom Construction in the Category of Finite Hypergraphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. Hom construction (dpeaa)DE-He213 Homotopy of hypergraph (dpeaa)DE-He213 Exponential hypergraph (dpeaa)DE-He213 Hypergraph homomorphism (dpeaa)DE-He213 Colorings of hypergraph (dpeaa)DE-He213 Maximum simple hypergraph (dpeaa)DE-He213 Wang, Yanying (orcid)0000-0001-9079-290X aut Zhang, Zhiguo aut Dai, Wei aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 4 vom: 30. Juni (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:4 day:30 month:06 https://dx.doi.org/10.1007/s00373-023-02672-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 4 30 06
allfieldsGer	10.1007/s00373-023-02672-6 doi (DE-627)SPR052103463 (SPR)s00373-023-02672-6-e DE-627 ger DE-627 rakwb eng Zhang, Conglei verfasserin aut Homotopy and Hom Construction in the Category of Finite Hypergraphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. Hom construction (dpeaa)DE-He213 Homotopy of hypergraph (dpeaa)DE-He213 Exponential hypergraph (dpeaa)DE-He213 Hypergraph homomorphism (dpeaa)DE-He213 Colorings of hypergraph (dpeaa)DE-He213 Maximum simple hypergraph (dpeaa)DE-He213 Wang, Yanying (orcid)0000-0001-9079-290X aut Zhang, Zhiguo aut Dai, Wei aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 4 vom: 30. Juni (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:4 day:30 month:06 https://dx.doi.org/10.1007/s00373-023-02672-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 4 30 06
allfieldsSound	10.1007/s00373-023-02672-6 doi (DE-627)SPR052103463 (SPR)s00373-023-02672-6-e DE-627 ger DE-627 rakwb eng Zhang, Conglei verfasserin aut Homotopy and Hom Construction in the Category of Finite Hypergraphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. Hom construction (dpeaa)DE-He213 Homotopy of hypergraph (dpeaa)DE-He213 Exponential hypergraph (dpeaa)DE-He213 Hypergraph homomorphism (dpeaa)DE-He213 Colorings of hypergraph (dpeaa)DE-He213 Maximum simple hypergraph (dpeaa)DE-He213 Wang, Yanying (orcid)0000-0001-9079-290X aut Zhang, Zhiguo aut Dai, Wei aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 4 vom: 30. Juni (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:4 day:30 month:06 https://dx.doi.org/10.1007/s00373-023-02672-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 4 30 06
language	English
source	Enthalten in Graphs and combinatorics 39(2023), 4 vom: 30. Juni volume:39 year:2023 number:4 day:30 month:06
sourceStr	Enthalten in Graphs and combinatorics 39(2023), 4 vom: 30. Juni volume:39 year:2023 number:4 day:30 month:06
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Hom construction Homotopy of hypergraph Exponential hypergraph Hypergraph homomorphism Colorings of hypergraph Maximum simple hypergraph
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container_title	Graphs and combinatorics
authorswithroles_txt_mv	Zhang, Conglei @@aut@@ Wang, Yanying @@aut@@ Zhang, Zhiguo @@aut@@ Dai, Wei @@aut@@
publishDateDaySort_date	2023-06-30T00:00:00Z
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author	Zhang, Conglei
spellingShingle	Zhang, Conglei misc Hom construction misc Homotopy of hypergraph misc Exponential hypergraph misc Hypergraph homomorphism misc Colorings of hypergraph misc Maximum simple hypergraph Homotopy and Hom Construction in the Category of Finite Hypergraphs
authorStr	Zhang, Conglei
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topic_title	Homotopy and Hom Construction in the Category of Finite Hypergraphs Hom construction (dpeaa)DE-He213 Homotopy of hypergraph (dpeaa)DE-He213 Exponential hypergraph (dpeaa)DE-He213 Hypergraph homomorphism (dpeaa)DE-He213 Colorings of hypergraph (dpeaa)DE-He213 Maximum simple hypergraph (dpeaa)DE-He213
topic	misc Hom construction misc Homotopy of hypergraph misc Exponential hypergraph misc Hypergraph homomorphism misc Colorings of hypergraph misc Maximum simple hypergraph
topic_unstemmed	misc Hom construction misc Homotopy of hypergraph misc Exponential hypergraph misc Hypergraph homomorphism misc Colorings of hypergraph misc Maximum simple hypergraph
topic_browse	misc Hom construction misc Homotopy of hypergraph misc Exponential hypergraph misc Hypergraph homomorphism misc Colorings of hypergraph misc Maximum simple hypergraph
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Homotopy and Hom Construction in the Category of Finite Hypergraphs
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title_full	Homotopy and Hom Construction in the Category of Finite Hypergraphs
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author_browse	Zhang, Conglei Wang, Yanying Zhang, Zhiguo Dai, Wei
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title_sort	homotopy and hom construction in the category of finite hypergraphs
title_auth	Homotopy and Hom Construction in the Category of Finite Hypergraphs
abstract	Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of d-colorings of a simple hypergraph %${\mathcal {H}}%$ could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and %${\mathcal {H}}%$. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Homotopy and Hom Construction in the Category of Finite Hypergraphs
url	https://dx.doi.org/10.1007/s00373-023-02672-6
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author2	Wang, Yanying Zhang, Zhiguo Dai, Wei
author2Str	Wang, Yanying Zhang, Zhiguo Dai, Wei
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doi_str	10.1007/s00373-023-02672-6
up_date	2024-07-04T01:17:19.381Z
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Homotopy and Hom Construction in the Category of Finite Hypergraphs

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