Enriched $\infty$-operads
In this paper we initiate the study of enriched $\infty$-operads. We introduce several models for these objects, including enriched versions of Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and Moerdijk, and show these are equivalent. Our main results are a version of Rezk...
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| creator | Chu, Hongyi Haugseng, Rune |
| description | In this paper we initiate the study of enriched $\infty$-operads. We
introduce several models for these objects, including enriched versions of
Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and
Moerdijk, and show these are equivalent. Our main results are a version of
Rezk's completion theorem for enriched $\infty$-operads: localization at the
fully faithful and essentially surjective morphisms is given by the full
subcategory of complete objects, and a rectification theorem: the homotopy
theory of $\infty$-operads enriched in the $\infty$-category arising from a
nice symmetric monoidal model category is equivalent to the homotopy theory of
strictly enriched operads. |
| doi_str_mv | 10.48550/arxiv.1707.08049 |
| format | Article |
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introduce several models for these objects, including enriched versions of
Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and
Moerdijk, and show these are equivalent. Our main results are a version of
Rezk's completion theorem for enriched $\infty$-operads: localization at the
fully faithful and essentially surjective morphisms is given by the full
subcategory of complete objects, and a rectification theorem: the homotopy
theory of $\infty$-operads enriched in the $\infty$-category arising from a
nice symmetric monoidal model category is equivalent to the homotopy theory of
strictly enriched operads.</description><identifier>DOI: 10.48550/arxiv.1707.08049</identifier><language>eng</language><subject>Mathematics - Algebraic Topology ; Mathematics - Category Theory</subject><creationdate>2017-07</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1707.08049$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1707.08049$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Chu, Hongyi</creatorcontrib><creatorcontrib>Haugseng, Rune</creatorcontrib><title>Enriched $\infty$-operads</title><description>In this paper we initiate the study of enriched $\infty$-operads. We
introduce several models for these objects, including enriched versions of
Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and
Moerdijk, and show these are equivalent. Our main results are a version of
Rezk's completion theorem for enriched $\infty$-operads: localization at the
fully faithful and essentially surjective morphisms is given by the full
subcategory of complete objects, and a rectification theorem: the homotopy
theory of $\infty$-operads enriched in the $\infty$-category arising from a
nice symmetric monoidal model category is equivalent to the homotopy theory of
strictly enriched operads.</description><subject>Mathematics - Algebraic Topology</subject><subject>Mathematics - Category Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzj0LgkAcgPFbGsL6AE01uGp3_u91DLEXEFocAznvhYQyOSPy20fW9GwPP4RWBKdUMoa3OrzbV0oEFimWmKo5WhVdaM3V2U18aTv_HOPk0bug7bBAM69vg1v-G6FqX1T5MSnPh1O-KxPNhUoaYknGoCFacaKsAcY9SNxIKsBmlDpOqDbGMyYaBkZQCtJ4hy1nSmoBEKH1bzvZ6j60dx3G-musJyN8AFxiNE8</recordid><startdate>20170725</startdate><enddate>20170725</enddate><creator>Chu, Hongyi</creator><creator>Haugseng, Rune</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20170725</creationdate><title>Enriched $\infty$-operads</title><author>Chu, Hongyi ; Haugseng, Rune</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-b1d1253b1a9619dc356f380b8473d244e614accf557b53c74438cfe0d6598a733</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Algebraic Topology</topic><topic>Mathematics - Category Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Chu, Hongyi</creatorcontrib><creatorcontrib>Haugseng, Rune</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Chu, Hongyi</au><au>Haugseng, Rune</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Enriched $\infty$-operads</atitle><date>2017-07-25</date><risdate>2017</risdate><abstract>In this paper we initiate the study of enriched $\infty$-operads. We
introduce several models for these objects, including enriched versions of
Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and
Moerdijk, and show these are equivalent. Our main results are a version of
Rezk's completion theorem for enriched $\infty$-operads: localization at the
fully faithful and essentially surjective morphisms is given by the full
subcategory of complete objects, and a rectification theorem: the homotopy
theory of $\infty$-operads enriched in the $\infty$-category arising from a
nice symmetric monoidal model category is equivalent to the homotopy theory of
strictly enriched operads.</abstract><doi>10.48550/arxiv.1707.08049</doi><oa>free_for_read</oa></addata></record> |
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| identifier | DOI: 10.48550/arxiv.1707.08049 |
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| subjects | Mathematics - Algebraic Topology Mathematics - Category Theory |
| title | Enriched $\infty$-operads |
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