Homological and homotopical epimorphisms in monoidal -categories
Federico Bambozzi
Source abstract
We compare homological and homotopical epimorphisms of associative algebras in monoidal -categories. Assume that geometric realizations and pushouts of associative algebras exist and that tensoring preserves geometric realizations. Then every homological epimorphism is homotopical. If, in addition, the ambient category is additive and tensoring preserves finite coproducts, the converse holds. This extends the result of Chuang and Lazarev for dg-algebras. In the symmetric monoidal setting, we discuss consequences for centers and commutative refinements, as well as applications to derived analytic geometry.
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