Moduli spaces of algebras over non-symmetric operads

Details Moduli spaces of algebras over non-symmetric operads Moduli spaces of algebras over non-symmetric operads

2011-12-21

arxiv.org/abs/1112.5146v1

Mathematics

Algebraic Topology

31 pages

Scientific paper

In this paper we study spaces of algebras over an operad (non-symmetric) in symmetric monoidal model categories. We begin by extending a result of Rezk for simplicial sets and simplicial modules to a general framework. We then apply this result to the construction of moduli stacks of algebras over an operad in a homotopical algebraic geometry context in the sense of To\"en and Vezzosi. We show that the stack of unital A-infinity algebras with a fixed underlying perfect complex is a formal Zariski open subset of the corresponding stack of non-necessarily unital A-infinity algebras. The analogue for associative algebra structures on a finite-dimensional vector space was noticed by Gabriel.

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