The euler characteristic of an enriched category

Kazunori Noguchi, Kohei Tanaka

Research output: Contribution to journalArticle

Abstract

We develop the homotopy theory of Euler characteristic (magnitude) of a category enriched in a monoidal model category. If a monoidal model category V is equipped with an Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler characteristic of V-enriched categories is also compatible with weak equivalences and fibrations in the canonical model structure on the category of V-enriched categories. In particular, we focus on the case of topological categories; i.e., categories enriched in 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).

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalTheory and Applications of Categories
Volume31
Publication statusPublished - 2016 Jan 3
Externally publishedYes

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Keywords

  • Enriched categories
  • Euler characteristic
  • Monoidal model categories

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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