The Euler characteristic of infinite acyclic categories with filtrations
Kazunori Noguchi
TL;DR
This paper defines the Euler characteristic for infinite acyclic categories with filtrations and proves its invariance under subdivision of finite categories, extending classical topological invariants to categorical structures.
Contribution
It introduces a new definition of Euler characteristic for infinite acyclic categories with filtrations and establishes its invariance under subdivision operations.
Findings
Defined Euler characteristic for infinite acyclic categories with filtrations
Proved invariance of the Euler characteristic under subdivision of finite categories
Extended topological invariants to categorical structures
Abstract
The aim of this paper is twofold. One is to give a definition of the Euler characteristic of infinite acyclic categories with filtrations and the other is to prove the invariance of the Euler characteristic under the subdivision of finite categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory