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Macquarie University  Department of Mathematics

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Categories in Algebra, Geometry and Mathematical Physics

Conference in honour of Ross Street's sixtieth birthday

July 11-16 2005, Macquarie University, Sydney

Sat, 16 July:  9:45 - 10:25

Using Segal categories to understand simplicial monoids and simplicial categories
Bergner, Julie (University of Notre Dame)

Much as Segal groupoids (and many other constructions) have been used to study simplicial or topological groups, we use Segal categories to better understand simplicial monoids. Specifically, there is a Quillen equivalence of model categories between a model structure on simplicial monoids and a ``reduced Segal category" model structure, a result which makes extensive use of algebraic theories. Using the more general notion of a multi-sorted algebraic theory the analogous result holds for simplicial categories with a fixed set of objects and Segal categories with the same set in degree zero. We can then apply the ideas behind this proof to prove that there is a Quillen equivalence between a model structure on the category of all small simplicial categories and a Segal category model structure.

Typeset PDF of this abstract.