Rigidification of algebras over multisorted theories
Abstract
We define the notion of a multisorted 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 multisorted theory and an appropriate model category structure on the category of functors from a multisorted 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2005
 arXiv:
 arXiv:math/0508152
 Bibcode:
 2005math......8152B
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Category Theory;
 18C10;
 18E35;
 18G30;
 55P48
 EPrint:
 This is the version published by Algebraic &