Coverings of small categories and nerves
Kazunori Noguchi

TL;DR
This paper explores the relationship between coverings of small categories and their nerves, establishing formulas for zeta functions and Euler characteristics in the context of finite categories and coverings.
Contribution
It introduces new formulas linking coverings of small categories with their nerves, including zeta functions and Euler characteristics.
Findings
Zeta function of E equals that of B to the number of sheets in the covering.
Euler characteristic of E equals the product of the Euler characteristics of the fiber and base categories.
Abstract
We prove a certain proposition which states a relationship between coverings of small categories and nerves. As its application, we prove that for a covering of finite categories, the zeta function of is the zeta function of to the number of sheet of . Moreover, we prove the formula for Euler characteristic of categories and coverings.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry
