TY - JOUR
T1 - The euler characteristic of an enriched category
AU - Noguchi, Kazunori
AU - Tanaka, Kohei
PY - 2016/1/3
Y1 - 2016/1/3
N2 - 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).
AB - 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).
KW - Enriched categories
KW - Euler characteristic
KW - Monoidal model categories
UR - http://www.scopus.com/inward/record.url?scp=84955578915&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84955578915&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84955578915
VL - 31
SP - 1
EP - 30
JO - Theory and Applications of Categories
JF - Theory and Applications of Categories
SN - 1201-561X
ER -