University of Sydney Algebra Seminar
Paula Verdugo
Friday 28 Apr, 12-1pm, Place: Carslaw 173
Fibrantly-induced model structures
Model categories provide, by abstracting fundamental properties of the category of topological spaces, a framework to do homotopy theory in diverse contexts. Since it is often hard to prove that something satifies the necessary properties to be a model structure, different techniques for constructing model structures on a given category C have been developed. One of these techniques --that has proved very useful-- is to right-induce a model structure through a right adjoint R:C \to M to a known model structure on M. In this case, the fibrations and weak equivalences in C are defined as the morphisms whose image under R is one such map in M. There are times, however, where this may be too restrictive, in the following sense. One may find themselves in a setting where one has a class of desired "fibrant objects" in C, and can describe fibrations and weak equivalences only between these fibrant objects. This inspires what we will call a fibrantly-induced model strucure. In this talk we will review the notion of model structures and see examples of them in algebraic settings before presenting the idea of fibrantly-induced model structures. If time allows, we will also see some examples. This is recent joint work with Leonard Guetta, Lyne Moser, and Maru Sarazola.