196 research outputs found
Rigidification of algebras over multi-sorted theories
We define the notion of a multi-sorted algebraic theory, which is a
generalization of an algebraic theory in which the objects are of different
"sorts." We prove a rigidification result for simplicial algebras over these
theories, showing that there is a Quillen equivalence between a model category
structure on the category of strict algebras over a multi-sorted theory and an
appropriate model category structure on the category of functors from a
multi-sorted theory to the category of simplicial sets. In the latter model
structure, the fibrant objects are homotopy algebras over that theory. Our two
main examples of strict algebras are operads in the category of simplicial sets
and simplicial categories with a given set of objects.Comment: This is the version published by Algebraic & Geometric Topology on 14
November 200
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