The homotopy theory of simplicial props

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.

Final version, to appear in Israel J. Math

References in corpus (9)

• Higher Topos Theory
• Dendroidal sets and simplicial operads
• Homotopy theory for algebras over polynomial monads
• Infinity Properads and Infinity Wheeled Properads
• On homotopy invariance for algebras over colored PROPs
• The Homotopy Theory of Simplicially Enriched Multicategories
• On the category of props
• Relative left properness of colored operads
• A simplicial model for infinity properads

Cited by in corpus (7)

• Dwyer--Kan homotopy theory for cyclic operads
• Labelled cospan categories and properads
• Dwyer-Kan Homotopy Theory of Algebras over Operadic Collections
• Lecture notes on infinity-properads
• The Dwyer-Kan model structure for enriched coloured PROPs
• A simplicial model for infinity properads
• Categorifying equivariant monoids