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

Fingerprint

Enriched Category
Euler Characteristic
Model Category
Monoidal Category
Fibration
Equivalence
Stratified Space
Topological Category
Canonical Model
Homotopy Theory
Topological space
Face
Computing

Keywords

  • Enriched categories
  • Euler characteristic
  • Monoidal model categories

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

The euler characteristic of an enriched category. / Noguchi, Kazunori; Tanaka, Kohei.

In: Theory and Applications of Categories, Vol. 31, 03.01.2016, p. 1-30.

Research output: Contribution to journalArticle

Noguchi, Kazunori ; Tanaka, Kohei. / The euler characteristic of an enriched category. In: Theory and Applications of Categories. 2016 ; Vol. 31. pp. 1-30.
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