# Central stability homology

## TL;DR

This paper introduces a new categorical framework for central stability homology, extending previous work to categories with infinite automorphism groups and linking it to broader stability concepts.

## Contribution

It develops a novel categorical approach to central stability homology, applicable to categories with infinite automorphisms, and connects it to existing stability theories.

## Key findings

- Provides a new categorical construction for central stability homology.
- Establishes a connection between central stability and homological stability.
- Develops a criterion for polynomial functors to be centrally stable.

## Abstract

We give a new categorical way to construct the central stability homology of Putman and Sam and explain how it can be used in the context of representation stability and homological stability. In contrast to them, we cover categories with infinite automorphism groups. We also connect central stability homology to Randal-Williams and Wahl's work on homological stability. We also develop a criterion that implies that functors that are polynomial in the sense of Randal-Williams and Wahl are centrally stable in the sense of Putman.