Félix Loubaton, Viktoriya Ozornova, Paula Verdugo, and I are organizing an iteration of the MPIM seminar on abstract homotopy theory. Please find the schedule below. An archive of past talks can also be found here.
The seminar usually takes place on Monday or Thursday, and we often go for lunch or dinner with the speaker after, for which you are of course also invited.
September 18, 11:30-12:30
David Kern (KTH Royal Institute of Technology), Codiscrete cofibrations vs iterated discrete fibrations for (∞,ℓ)-congruences
March 5, 16:30-17:30
Johannes Gloßner (Universität Regensburg), Model-independent lax 2-functors
March 19, 16:30-17:30
Hugo Pourcelot (Università degli studi di Firenze), Dioperads, Frobenius monoidal functors and integration along fibers
May 28, 15:00-16:00
Informal session, please find the program below.
June 4, 16:30-17:30
Michael Ching (Amherst College), Differential bundles in Goodwillie calculus
June 18, 16:30-17:30
Luuk Stehouwer (Dalhousie University), The K-theory of graded rings
June 30 - July 11
No seminar due to the workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras
July 13 - July 19
No seminar due to the International category theory conference
July 23, 16:30-17:30
David Gepner (Johns Hopkins University), The Gray tensor product of infinity categories and basic tensor-enriched category theory
Summer break
15:00-15:30, Jaco Ruit: A universal approach to colimit completions of generalized ∞-categories
I will give a short presentation about work-in-progress concerning colimit completions of different flavors of ∞-categories, such as enriched and indexed ∞-categories. To this end, I will start by sketching an abstract theory of presheaf objects and cocompletions in ∞-equipments, and then sketch how one may construct presheaf objects in Morita ∞-equipments. The latter part can be specialized to the Morita ∞-equipments associated to double ∞-categories of spans and matrices, to recover the existence of cocompletions for indexed and enriched ∞-categories.
15:30-16:00, Thomas Blom: Virtual span ∞-categories and virtual Morita ∞-categories
Spans are composed via pullbacks. As such, defining the span ∞-category of an ∞-category C requires the assumption that C admits pullbacks.
A similar situation arises when defining the Morita ∞-category of a monoidal ∞-category: composition is given by relative tensor products, which are specific types of geometric realizations. It therefore seems necessary to assume that C admits these geometric realizations and that the monoidal structure preserves them.
In this talk, we will eliminate of these assumptions. The trade-off is that we need to redefine what we mean by an ∞-category.