Props in model categories and homotopy invariance of structures

By Benoit Fresse. 2008

53 citations recorded by the source corpus.

Abstract We prove that any category of props in a symmetric monoidal model category inherits a model structure. We devote an appendix, about half the size of the paper, to the proof of the model category axioms in a general setting. We need the general argument to address the case of props in topological spaces and dg-modules over an arbitrary ring, but we give a less technical proof which applies to the category of props in simplicial sets, simplicial modules, and dg-modules over a ring of characteristic 0. We apply the model structure of props to the homotopical study of algebras over a prop. Our goal is to prove that an object 𝑋 homotopy equivalent to an algebra 𝐴 over a cofibrant prop P inherits a P-algebra structure so that 𝑋 defines a model of 𝐴 in the homotopy category of P-algebras. In the differential graded context, this result leads to a generalization of Kadeishvili's minimal model of 𝐴∞-algebras.

Subfields: Geometry and Topology, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/73a76c0ee22e614106cf9542f29722e26164bdfa

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Citations in the corpus

Homotopy theory for algebras over polynomial monads (2013, unknown): “There is an obstruction for the existence of model structure on symmetric operads with coefficient in chain complexes over a field of positive characteristic, similarly to (12.30), which was first described by Fresse [22].”
Pre-Lie deformation theory (2015, methodology): “We reproduce here quickly the main ingredient of the proof of [Fre10, Theorem 7.3 (2)] since we will use it in the sequel.”