Geodesic
The Euler characteristic of an enriched category
Theory and applications of categories, Tome 31 (2016), pp. 1-30

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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 $C(X)$.

Publié le :
Classification : 18D20, 55U35
Keywords: Euler characteristic, enriched categories, monoidal model categories 
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     author = {Kazunori Noguchi and Kohei Tanaka},
     title = {The {Euler} characteristic of an enriched category},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2016_31_a0/}
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Kazunori Noguchi; Kohei Tanaka. The Euler characteristic of an enriched category. Theory and applications of categories, Tome 31 (2016), pp. 1-30. http://geodesic.mathdoc.fr/item/TAC_2016_31_a0/