Classifying spaces of algebras over a prop

Sinan Yalin (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We prove that a weak equivalence between cofibrant props induces a weak equivalence between the associated classifying spaces of algebras. This statement generalizes to the prop setting a homotopy invariance result which is well known in the case of algebras over operads. The absence of model category structure on algebras over a prop leads us to introduce new methods to overcome this difficulty. We also explain how our result can be extended to algebras over colored props in any symmetric monoidal model category tensored over chain complexes.

Mots clés: bialgebras category; classifying space; homotopy invariance; prop

Domaines: Topologie algébrique [math.AT]

Sinan Yalin. Classifying spaces of algebras over a prop. Algebraic and Geometric Topology, 2014, 14 (5), pp.2561-2593. ⟨hal-00717281v4⟩