ATCAT seminar - "Model bicategories and their homotopy bicategories (Joint work with M.E. Descotte and E.J. Dubuc)"
Speaker : Martin Szyld, Dalhousie University
I will present a generalization of the concept of model category to the context of bicategories as well as a corresponding localization construction. The axioms for a model bicategory are a natural generalization to bicategories of those given by Quillen in the sense that they are obtained by requiring the diagrams to commute up to invertible 2-cells, and by considering a 2-dimensional aspect of the lifting properties which relate these families of arrows (in particular, when we consider a category as a bicategory, the two notions coincide: it will be a model bicategory if and only if it is a model category).
I will define the homotopy bicategory associated to a model bicategory C, whose 2-cells are given by homotopies in C. I will also describe a fibrant-cofibrant replacement for model bicategories, and, time permitting, I will show how we have proved that this yields the localization of C (in the bicategorical sense) at the weak equivalences. Our proof of this result uses a "transport of structure"; the application of this technique in this context is, as far as we know, a novel method.
Ellen LynchATCAT seminar - "Model bicategories and their homotopy bicategories (Joint work with M.E. Descotte and E.J. Dubuc)"