On the Mac Lane $Q$-Construction for Exact $\infty$-Categories

Ettore Aldrovandi; Arash Karimi

On the Mac Lane $Q$-Construction for Exact $\infty$-Categories

Algebraic Topology 2025-01-29 v2 Category Theory K-Theory and Homology

Authors: Ettore Aldrovandi , Arash Karimi

Abstract

We extend McCarthy's stabilization construction to exact $\infty$ -categories. This is achieved by constructing, for any functor from exact $\infty$ -categories to a fixed stable $\infty$ -category $\mathcal{A}$ , a coherent chain complex in $\mathcal{A}$ that is an immediate generalization of Mac Lane's cubical $Q$ -complex computing the stable homology of abelian groups.

Keywords

stable categories category theory homotopy theory

Cite

@article{arxiv.2501.16259,
  title  = {On the Mac Lane $Q$-Construction for Exact $\infty$-Categories},
  author = {Ettore Aldrovandi and Arash Karimi},
  journal= {arXiv preprint arXiv:2501.16259},
  year   = {2025}
}

Comments

Updated one reference, fixed processing that led to missing references

On the Mac Lane $Q$-Construction for Exact $\infty$-Categories

Abstract

Keywords

Cite

Comments

Related papers