Title: Rigidification of algebras over multi-sorted algebraic
theories
Author: Julia E. Bergner
Author's e-mail address: bergnerj@member.ams.org
AMS Classification: 18C10, 18G30, 18E35, 55P48
arXiv submission number: math.AT/0508152
Author's address:
Kansas State University
138 Cardwell Hall
Manhattan, KS 66506
Abstract: 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.