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Segal enriched categories and applications
Theory and applications of categories, Tome 35 (2020), pp. 1227-1267 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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In this paper we develop a theory of Segal enriched categories. Our motivation was to generalize the notion of up-to-homotopy monoid in a monoidal category, introduced by Leinster. Our formalism generalizes the classical theory of Segal categories and extends the theory of categories enriched over a 2-category. We introduce Segal dg-categories which did not exist so far. We show that the homotopy transfer problem for algebras leads directly to a Leinster-Segal algebra.

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Classification : 18D20, 18G30, 18N10, 18N40, 18N45, 18N60
Keywords: Segal categories, enriched categories, homotopy algebras, higher categories 
@article{TAC_2020_35_a32,
     author = {Hugo V. Bacard},
     title = {Segal enriched categories and applications},
     journal = {Theory and applications of categories},
     pages = {1227--1267},
     year = {2020},
     volume = {35},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a32/}
}
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Hugo V. Bacard. Segal enriched categories and applications. Theory and applications of categories, Tome 35 (2020), pp. 1227-1267. http://geodesic.mathdoc.fr/item/TAC_2020_35_a32/