\v{C}ech complexes for covers of small categories
Kohei Tanaka

TL;DR
This paper introduces a combinatorial analogue of the nerve theorem for small categories using the Grothendieck construction, and applies it to establish an inclusion-exclusion principle for the Euler characteristic of finite categories.
Contribution
It develops a new combinatorial approach to the nerve theorem for small categories and proves an inclusion-exclusion principle for their Euler characteristic.
Findings
Established a combinatorial nerve theorem analogue for small categories
Proved the inclusion-exclusion principle for Euler characteristics of finite categories
Applied Grothendieck construction to categorical covers
Abstract
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 principle for the Euler characteristic of a finite category.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Geometric and Algebraic Topology
