Thomason cohomology of categories
We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small category, and coincide with Gabriel–Zisman cohomology and homology of the sim...
Gespeichert in:
| Veröffentlicht in: | Journal of pure and applied algebra 2013-11, Vol.217 (11), p.2163-2179 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2179 |
|---|---|
| container_issue | 11 |
| container_start_page | 2163 |
| container_title | Journal of pure and applied algebra |
| container_volume | 217 |
| creator | Gálvez-Carrillo, Imma Neumann, Frank Tonks, Andrew |
| description | We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small category, and coincide with Gabriel–Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues–Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories. |
| doi_str_mv | 10.1016/j.jpaa.2013.02.005 |
| format | Article |
| fullrecord | <record><control><sourceid>csuc_cross</sourceid><recordid>TN_cdi_csuc_recercat_oai_recercat_cat_2072_211769</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0022404913000364</els_id><sourcerecordid>oai_recercat_cat_2072_211769</sourcerecordid><originalsourceid>FETCH-LOGICAL-c386t-4c83b4ecd1d0b33d78ca4b920d5f9fc2a73370fb4853a7e8873f93889f8c2f1f3</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKt_wFP9AbtOPrrJghcpfkHBSz0P2dmkZmmbklTBf2-WFrx5GGYG5pl552XslkPNgTf3Qz3sra0FcFmDqAHmZ2zCjZYVl7o5ZxMAISoFqr1kVzkPAGVSNRN2t_qMW5vjbkaxVHET1z-z6GdkD24dU3D5ml14u8nu5pSn7OP5abV4rZbvL2-Lx2VF0jSHSpGRnXLU8x46KXttyKquFdDPfetJWC2lBt8pM5dWO1O0-VYa03pDwnMvp4wf91L-IkyOXCoiMNrw14whQAsUnOumLYw4MSnmnJzHfQpbm36QA47G4ICjMTgagyCwGFOghyPkyjffwSXMFNyOXB_KoQP2MfyH_wJbgmsk</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Thomason cohomology of categories</title><source>Recercat</source><source>Elsevier ScienceDirect Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Gálvez-Carrillo, Imma ; Neumann, Frank ; Tonks, Andrew</creator><creatorcontrib>Gálvez-Carrillo, Imma ; Neumann, Frank ; Tonks, Andrew</creatorcontrib><description>We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small category, and coincide with Gabriel–Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues–Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.</description><identifier>ISSN: 0022-4049</identifier><identifier>EISSN: 1873-1376</identifier><identifier>DOI: 10.1016/j.jpaa.2013.02.005</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>18 Category theory; homological algebra ; 18D Categories with structure ; 18G Homological algebra ; 55 Algebraic topology ; 55U Applied homological algebra and category theory ; Algebra, Homological ; Classificació AMS ; Homologia ; Homology theory ; K-teoria ; K-theory ; Matemàtiques i estadística ; Teoria de categories; àlgebra homològica ; Àlgebra ; Àlgebra homològica ; Àrees temàtiques de la UPC</subject><ispartof>Journal of pure and applied algebra, 2013-11, Vol.217 (11), p.2163-2179</ispartof><rights>2013 Elsevier B.V.</rights><rights>info:eu-repo/semantics/openAccess</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c386t-4c83b4ecd1d0b33d78ca4b920d5f9fc2a73370fb4853a7e8873f93889f8c2f1f3</citedby><cites>FETCH-LOGICAL-c386t-4c83b4ecd1d0b33d78ca4b920d5f9fc2a73370fb4853a7e8873f93889f8c2f1f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0022404913000364$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,26951,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Gálvez-Carrillo, Imma</creatorcontrib><creatorcontrib>Neumann, Frank</creatorcontrib><creatorcontrib>Tonks, Andrew</creatorcontrib><title>Thomason cohomology of categories</title><title>Journal of pure and applied algebra</title><description>We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small category, and coincide with Gabriel–Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues–Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.</description><subject>18 Category theory; homological algebra</subject><subject>18D Categories with structure</subject><subject>18G Homological algebra</subject><subject>55 Algebraic topology</subject><subject>55U Applied homological algebra and category theory</subject><subject>Algebra, Homological</subject><subject>Classificació AMS</subject><subject>Homologia</subject><subject>Homology theory</subject><subject>K-teoria</subject><subject>K-theory</subject><subject>Matemàtiques i estadística</subject><subject>Teoria de categories; àlgebra homològica</subject><subject>Àlgebra</subject><subject>Àlgebra homològica</subject><subject>Àrees temàtiques de la UPC</subject><issn>0022-4049</issn><issn>1873-1376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>XX2</sourceid><recordid>eNp9kE1LAzEQhoMoWKt_wFP9AbtOPrrJghcpfkHBSz0P2dmkZmmbklTBf2-WFrx5GGYG5pl552XslkPNgTf3Qz3sra0FcFmDqAHmZ2zCjZYVl7o5ZxMAISoFqr1kVzkPAGVSNRN2t_qMW5vjbkaxVHET1z-z6GdkD24dU3D5ml14u8nu5pSn7OP5abV4rZbvL2-Lx2VF0jSHSpGRnXLU8x46KXttyKquFdDPfetJWC2lBt8pM5dWO1O0-VYa03pDwnMvp4wf91L-IkyOXCoiMNrw14whQAsUnOumLYw4MSnmnJzHfQpbm36QA47G4ICjMTgagyCwGFOghyPkyjffwSXMFNyOXB_KoQP2MfyH_wJbgmsk</recordid><startdate>20131101</startdate><enddate>20131101</enddate><creator>Gálvez-Carrillo, Imma</creator><creator>Neumann, Frank</creator><creator>Tonks, Andrew</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>XX2</scope></search><sort><creationdate>20131101</creationdate><title>Thomason cohomology of categories</title><author>Gálvez-Carrillo, Imma ; Neumann, Frank ; Tonks, Andrew</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c386t-4c83b4ecd1d0b33d78ca4b920d5f9fc2a73370fb4853a7e8873f93889f8c2f1f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>18 Category theory; homological algebra</topic><topic>18D Categories with structure</topic><topic>18G Homological algebra</topic><topic>55 Algebraic topology</topic><topic>55U Applied homological algebra and category theory</topic><topic>Algebra, Homological</topic><topic>Classificació AMS</topic><topic>Homologia</topic><topic>Homology theory</topic><topic>K-teoria</topic><topic>K-theory</topic><topic>Matemàtiques i estadística</topic><topic>Teoria de categories; àlgebra homològica</topic><topic>Àlgebra</topic><topic>Àlgebra homològica</topic><topic>Àrees temàtiques de la UPC</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gálvez-Carrillo, Imma</creatorcontrib><creatorcontrib>Neumann, Frank</creatorcontrib><creatorcontrib>Tonks, Andrew</creatorcontrib><collection>CrossRef</collection><collection>Recercat</collection><jtitle>Journal of pure and applied algebra</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gálvez-Carrillo, Imma</au><au>Neumann, Frank</au><au>Tonks, Andrew</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Thomason cohomology of categories</atitle><jtitle>Journal of pure and applied algebra</jtitle><date>2013-11-01</date><risdate>2013</risdate><volume>217</volume><issue>11</issue><spage>2163</spage><epage>2179</epage><pages>2163-2179</pages><issn>0022-4049</issn><eissn>1873-1376</eissn><abstract>We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small category, and coincide with Gabriel–Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues–Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.jpaa.2013.02.005</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-4049 |
| ispartof | Journal of pure and applied algebra, 2013-11, Vol.217 (11), p.2163-2179 |
| issn | 0022-4049 1873-1376 |
| language | eng |
| recordid | cdi_csuc_recercat_oai_recercat_cat_2072_211769 |
| source | Recercat; Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | 18 Category theory homological algebra 18D Categories with structure 18G Homological algebra 55 Algebraic topology 55U Applied homological algebra and category theory Algebra, Homological Classificació AMS Homologia Homology theory K-teoria K-theory Matemàtiques i estadística Teoria de categories àlgebra homològica Àlgebra Àlgebra homològica Àrees temàtiques de la UPC |
| title | Thomason cohomology of categories |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-08T20%3A52%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-csuc_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Thomason%20cohomology%20of%20categories&rft.jtitle=Journal%20of%20pure%20and%20applied%20algebra&rft.au=G%C3%A1lvez-Carrillo,%20Imma&rft.date=2013-11-01&rft.volume=217&rft.issue=11&rft.spage=2163&rft.epage=2179&rft.pages=2163-2179&rft.issn=0022-4049&rft.eissn=1873-1376&rft_id=info:doi/10.1016/j.jpaa.2013.02.005&rft_dat=%3Ccsuc_cross%3Eoai_recercat_cat_2072_211769%3C/csuc_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_els_id=S0022404913000364&rfr_iscdi=true |