Homology of higher categories

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.