A combinatorial construction of homology via ACGW categories
Abstract
This paper introduces the reader to the key ideas and techniques for working with ACGW categories, a recently introduced framework for algebraic K K -theory. To do so, we focus on how homology theory generalizes to ACGW categories, particularly in the central example of finite sets. We show how the ACGW formalism can be used to produce various classical homological algebra results such as the Snake Lemma and long exact sequences of relative pairs.
Fields of Study & Subjects
Data Management and Algorithms
Topological and Geometric Data Analysis
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 159–191
- Publication date
- 1 January 2026
- Language
- EN