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# Macquarie University  Department of Mathematics

## Categories in Algebra, Geometry and Mathematical Physics

### Conference in honour of Ross Street's sixtieth birthday

#### July 11-16 2005, Macquarie University, Sydney

Mon, 11 July:  16:30 - 17:20

##### Homotopy theory of small functors over large categories
###### Chorny, Boris (University of Western Ontario)

We consider the category of small simplicial functors from a large indexing category to the category of simplicial sets. If the indexing category is cocomplete we construct a model category structure on this object with weak equivalences and fibrations being objectwise. We discuss some applications of this model category.

If the indexing category is $\cal S^{\mathrm{op}}$, then we identify, through the Quillen equivalence, the category of small simplicial contravariant functors from simplicial sets to simplicial sets with the category of maps of spaces equipped with the equivariant model structure.

Typeset PDF of this abstract.