Homology of higher categories
Algebraic Topology
2026-05-08 v2 Category Theory
K-Theory and Homology
Abstract
Homology is characterized by the Eilenberg-Steenrod axioms. We define homology of higher categories via a categorical analogue of the Eilenberg-Steenrod axioms. We prove a categorical Dold-Kan correspondence, providing a combinatorial presentation of categorical homology in which the Street nerve plays the role of the singular complex. This implies a categorical Dold-Thom theorem that endows categorical homology with a multiplicative structure and leads to computations of categorical homology of the globes.
Keywords
Cite
@article{arxiv.2505.22640,
title = {Homology of higher categories},
author = {Hadrian Heine},
journal= {arXiv preprint arXiv:2505.22640},
year = {2026}
}
Comments
Second part of arXiv:2505.22640, which got splitted