The homotopy theory of simplicial props

TL;DR

This paper establishes a model category structure on the category of small colored simplicial props, extending the homotopy theory framework for algebraic structures like operads and categories.

Contribution

It introduces a cofibrantly generated model structure on simplicial props, enabling homotopical analysis of these algebraic objects.

Findings

The category of small colored simplicial props admits a cofibrantly generated model structure.

The forgetful functor from props to operads is a right Quillen functor.

Provides foundational tools for homotopy theory of higher algebraic structures.

Abstract

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher props," we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.