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Left properness and Strictification of co-Segal dg-categories

Hugo Bacard
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Abstract

We study co-Segal dg-categories over a general commutative ring that is not necessarily a field. We show that for any set X there is a model structure on co-Segal dg-categories over X that is always left proper. We show that the corresponding homotopy category is equivalent to the homotopy category of usual dg-categories over X. This result will be shown to extend naturally when we vary the set of objects. We also extend the co-Segal formalism to algebras and categories over an operad P. The results of the paper are established for co-Segal M-categories enriched over any symmetric monoidal model category M = (M,⊗,I) whose underlying model category is combinatorial and left proper. We conjecture that the co-Segal formalism for algebras over an operad should bypass the limitation of having a field of characteristic zero to get a homotopy theory for commutative (co-Segal) dg-algebras.
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Dates and versions

hal-00996801 , version 1 (27-05-2014)

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  • HAL Id : hal-00996801 , version 1

Cite

Hugo Bacard. Left properness and Strictification of co-Segal dg-categories. 2014. ⟨hal-00996801⟩

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