1,469 research outputs found
A model structure on the category of small categories for coverings
We define a new model structure on the category of small categories, which is
intimately related to the notion of coverings and fundamental groups of small
categories. Fibrant objects in the model structure coincide with groupoids, and
the fibrant replacement is the groupoidification.Comment: 16 page
The Euler characteristic of an enriched category
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
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