Completion under strong homotopy cokernels

TL;DR

This paper demonstrates that embedding a category with finite colimits into its arrow category yields the completion under strong homotopy cokernels, utilizing the nullhomotopy structure from canonical adjunctions.

Contribution

It establishes that the arrow category embedding provides a universal completion under strong homotopy cokernels for categories with finite colimits.

Findings

Embedding into Arr(A) yields the completion under strong homotopy cokernels.

Nullhomotopy structure is induced by canonical adjunctions.

Provides a categorical framework for homotopy cokernels.

Abstract

For A a category with finite colimits, we show that the embedding of A into the category of arrows Arr(A) determined by the initial object is the completion of A under strong homotopy cokernels. The nullhomotopy structure of Arr(A) (needed in order to express the notion of homotopy cokernel) is the usual one induced by the canonical string of adjunctions between A and Arr(A).