Double categorical model of $(\infty,1)$-categories
Building on work by Fiore-Pronk-Paoli, we construct four model structures on the category of double categories, each modeling one of the following: simplicial spaces, Segal spaces, $(\infty,1)$-categories, and $\infty$-groupoids. Additionally, we provide an explicit formula for computing homotopy co...
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| creator | Guetta, Léonard Moser, Lyne |
| description | Building on work by Fiore-Pronk-Paoli, we construct four model structures on
the category of double categories, each modeling one of the following:
simplicial spaces, Segal spaces, $(\infty,1)$-categories, and
$\infty$-groupoids. Additionally, we provide an explicit formula for computing
homotopy colimits in these models using the Grothendieck construction. We
expect the model of double categories for $(\infty,1)$-categories to play a
similar role than that of the model of categories for spaces or
$\infty$-groupoids in Grothendieck's study of the homotopy theory of spaces. |
| doi_str_mv | 10.48550/arxiv.2412.15715 |
| format | Article |
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the category of double categories, each modeling one of the following:
simplicial spaces, Segal spaces, $(\infty,1)$-categories, and
$\infty$-groupoids. Additionally, we provide an explicit formula for computing
homotopy colimits in these models using the Grothendieck construction. We
expect the model of double categories for $(\infty,1)$-categories to play a
similar role than that of the model of categories for spaces or
$\infty$-groupoids in Grothendieck's study of the homotopy theory of spaces.</description><identifier>DOI: 10.48550/arxiv.2412.15715</identifier><language>eng</language><subject>Mathematics - Algebraic Topology ; Mathematics - Category Theory</subject><creationdate>2024-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2412.15715$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2412.15715$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Guetta, Léonard</creatorcontrib><creatorcontrib>Moser, Lyne</creatorcontrib><title>Double categorical model of $(\infty,1)$-categories</title><description>Building on work by Fiore-Pronk-Paoli, we construct four model structures on
the category of double categories, each modeling one of the following:
simplicial spaces, Segal spaces, $(\infty,1)$-categories, and
$\infty$-groupoids. Additionally, we provide an explicit formula for computing
homotopy colimits in these models using the Grothendieck construction. We
expect the model of double categories for $(\infty,1)$-categories to play a
similar role than that of the model of categories for spaces or
$\infty$-groupoids in Grothendieck's study of the homotopy theory of spaces.</description><subject>Mathematics - Algebraic Topology</subject><subject>Mathematics - Category Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMjE00jM0NTc05WQwdskvTcpJVUhOLElNzy_KTE7MUcjNT0nNUchPU1DRiMnMSyup1DHUVNGFqUgt5mFgTUvMKU7lhdLcDPJuriHOHrpg4-MLijJzE4sq40HWxIOtMSasAgCBUzDJ</recordid><startdate>20241220</startdate><enddate>20241220</enddate><creator>Guetta, Léonard</creator><creator>Moser, Lyne</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20241220</creationdate><title>Double categorical model of $(\infty,1)$-categories</title><author>Guetta, Léonard ; Moser, Lyne</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2412_157153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Algebraic Topology</topic><topic>Mathematics - Category Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Guetta, Léonard</creatorcontrib><creatorcontrib>Moser, Lyne</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Guetta, Léonard</au><au>Moser, Lyne</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Double categorical model of $(\infty,1)$-categories</atitle><date>2024-12-20</date><risdate>2024</risdate><abstract>Building on work by Fiore-Pronk-Paoli, we construct four model structures on
the category of double categories, each modeling one of the following:
simplicial spaces, Segal spaces, $(\infty,1)$-categories, and
$\infty$-groupoids. Additionally, we provide an explicit formula for computing
homotopy colimits in these models using the Grothendieck construction. We
expect the model of double categories for $(\infty,1)$-categories to play a
similar role than that of the model of categories for spaces or
$\infty$-groupoids in Grothendieck's study of the homotopy theory of spaces.</abstract><doi>10.48550/arxiv.2412.15715</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Topology Mathematics - Category Theory |
| title | Double categorical model of $(\infty,1)$-categories |
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