A Quillen model category structure on some categories of comonoids

TL;DR

This paper demonstrates that under specific conditions, categories of comonoids in certain monoidal model categories can themselves be equipped with a compatible model structure, expanding the applicability of homotopical methods.

Contribution

It establishes a Quillen model category structure on categories of comonoids within certain monoidal model categories, a novel extension of model category theory.

Findings

Comonoid categories inherit model structures under specific conditions.

The results apply to a class of monoidal model categories.

Provides a framework for homotopical analysis of comonoids.

Abstract

We prove that for certain monoidal (Quillen) model categories, the category of comonoids therein also admits a model structure.