Graduate Category Theory Seminar

Currently the category theory seminar is organized by Patrick Nicodemus, nicodemus@math.wisc.edu. There is a mailing list, join-categorytheory@lists.wisc.edu, which sends out announcements on about a weekly basis. In person meetings are cancelled indefinitely due to coronavirus.

Spring 2018

• Week One - Plan of seminar established. Definition of Kan extension; colimit formula for the Kan extension. Following Mac Lane's Categories for the Working Mathematician.
• Week Two - Properties of Kan extensions.
• Week Three - Coends, examples of coends. The coend formula for the Kan extension.
• Week Four - Definition of a simplicial set. The Density theorem, phrased in terms of Kan extensions but illustrated in the case of simplicial sets.
• Week Five - the "nerve-realization adjunction" theorem (which occurs as I.5.2 in Mac Lane and Moerdijk, "Sheaves in Geometry and Logic") phrased in terms of the left Kan extension of the functor A : C -> E along the Yoneda embedding. Some examples of the theorem: the adjunction between presheaves over X and Top/X, the adjunction between the singular total complex functor from simplicial sets.
• Week Six - Spring break.
• Week Seven - First online session due to Coronavirus. The Nerve of a Small Category and the Fundamental Groupoid of a Simplicial Set, available here.
• Week Eight (Planned) - Geometry of simplicial sets. Whence degeneracies? The Eilenberg-Zilber theorem. Acyclic Models.