9 citations · 19 across the 12 of their papers we have counts for
4 papers · 1 filter
Čech complexes for covers of small categories
Kohei Tanaka
We present a combinatorial analogue of the nerve theorem for covers of small categories, using the Grothendieck construction. We apply our result to prove the inclusion-exclusion p…
The Euler characteristic of a bicategory and the product formula for fibered bicategories
Kohei Tanaka
This paper studies the Euler characteristic of a bicategory based on the concept of magnitudes introduced by Leinster. We focus on its invariance with respect to biequivalence and…
The Euler characteristic of an enriched category
Kazunori Noguchi, Kohei Tanaka
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 wea…
A model structure on the category of small categories for coverings
Kohei Tanaka
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 obje…