Combinatorial Categorical Equivalences
نویسنده
چکیده
In this paper we prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let X denote an additive category with finite direct sums and splitting idempotents. The class includes (a) the Dold-Puppe-Kan theorem that simplicial objects in X are equivalent to chain complexes in X ; (b) the observation of Church-Ellenberg-Farb that X -valued species are equivalent to X -valued functors from the category of finite sets and injective partial functions; (c) a DoldKan-type result of Pirashvili concerning Segal’s category Γ; and so on. We provide a construction which produces further examples.
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