2014/05/14 by Kazunori Noguchi, Kohei Tanaka, Noguchi, Kazunori +1
Mathematics · #18D20 #55U35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1405.3356
openalex publication_date 2014/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define Euler characteristic of a category enriched by a monoidal model category. If a monoidal model category V is equipped with Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler characteristic is also compatible with weak equivalences and fibrations in the model structure induced by that of V. In particular, we focus on the case of topological categories; that is, categories enriched by the category of topological spaces. As its application, we obtain the ordinary Euler characteristic of a cellular stratified space X by computing the Euler characteristic of the face category C(X) induced from X.