Title: Systems of homotopy colimits
Abstract: Limits and colimit constructions are ubiquitous in category theory, and are one of the main tools used to understand how objects in a category relate to one another. These are very concrete and easily stated in terms of universal properties: given a diagram in a category, the colimit is the initial cocone making the resulting diagram commute. Homotopy colimits, on the other hand, have always been more difficult to define. These so not satisfy a universal property in any category, and tend to be described in terms of a construction and properties. In recent work with Brooks-Hess-Johnson-Rasmusen-Schreiner (BBHJRS for short) we attempted to enumerate the properties required for something to be a system of homotopy colimits. Following a referee’s comments, we transformed the list into a more familiar categorical construction. In this talk, I will offer an alternative definition of homotopy colimits using actegories.
