Moduli spaces of algebras over non-symmetric operads
In this paper we study spaces of algebras over an operad (nonsymmetric) 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...
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41878 |
| Acesso em linha: | http://hdl.handle.net/11441/41878 https://doi.org/10.2140/agt.2014.14.1489 |
| Access Level: | acceso abierto |
| Palavra-chave: | operad algebra associative algebra unital algebra model category mapping space moduli stack |
| Resumo: | In this paper we study spaces of algebras over an operad (nonsymmetric) 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 To¨en 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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