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Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories
Theory and applications of categories, Tome 38 (2022), pp. 1156-1208 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced functor between categories of algebras is an equivalence of homotopy theories. We describe an application to ring categories.

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Classification : Primary: 18M65, Secondary: 55P42, 18M05
Keywords: multicategory, permutative category, homotopy equivalence, operad algebra 
@article{TAC_2022_38_a29,
     author = {Niles Johnson and Donald Yau},
     title = {Homotopy {Equivalent} {Algebraic} {Structures} in {Multicategories} and {Permutative} {Categories}},
     journal = {Theory and applications of categories},
     pages = {1156--1208},
     year = {2022},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a29/}
}
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Niles Johnson; Donald Yau. Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories. Theory and applications of categories, Tome 38 (2022), pp. 1156-1208. http://geodesic.mathdoc.fr/item/TAC_2022_38_a29/