Moduli spaces of algebras over non-symmetric operads

Fernando Muro

doi:10.2140/agt.2014.14.229

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arXiv · 1112.5146

Moduli spaces of algebras over non-symmetric operads

Fernando Muro

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Abstract

In this paper we study spaces of algebras over an operad (non-symmetric) in symmetric monoidal model categories. We first compute the homotopy fiber of the forgetful functor sending an algebra to its underlying object, extending a result of Rezk. We then apply this computation to the construction of geometric moduli stacks of algebras over an operad in a homotopical algebraic geometry context in the sense of Toën and Vezzosi. We show under mild hypotheses that the moduli stack of unital associative algebras is a Zariski open substack of the moduli stack of non-necessarily unital associative algebras. The classical analogue for finite-dimensional vector spaces was noticed by Gabriel.

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BibTeX RIS

Fernando Muro. 2013-08-19. Moduli spaces of algebras over non-symmetric operads. https://doi.org/10.2140/agt.2014.14.229

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