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Online seminář z algebry - 26.11.2020 PDF Tisk

Další seminář z algebry se koná 26.11.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Martin Bidlingmaier (Aarhus University)

Model categories of lcc categories and the gros model of dependent type theory

In this talk we discuss various model categories of locally cartesian closed (lcc) categories and their relevance to coherence problems, in particular the coherence problem of categorical semantics of dependent type theory. We begin with Lcc, the model category of locally cartesian closed (lcc) sketches. Its fibrant objects are precisely the lcc categories, though without assigned choices of universal objects. We then obtain a Quillen equivalent model category sLcc of strict lcc categories as the category of algebraically fibrant objects of Lcc. Strict lcc categories are categories with assigned choice of lcc structure, and their morphisms preserve these choices on the nose. Conjecturally, sLcc is precisely Lack’s model category of algebras for a  2-monad T, where T is instantiated with the free lcc category functor on Cat. We then discuss the category of algebraically cofibrant objects of sLcc and show how it can serve as a “gros” model of dependent type theory.

Aktualizováno Středa, 25 Listopad 2020 10:33
Online seminář z algebry - 19.11.2020 PDF Tisk

Další seminář z algebry se koná 19.11.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Maru Sarazola (Cornell University)

The stable homotopy hypothesis

The homotopy hypothesis is a well-known bridge between topology and category theory. Its most general formulation, due to Grothendieck, asserts that topological spaces should be "the same" as infinity-groupoids. In the stable version of the homotopy hypothesis, topological spaces are replaced with spectra.

In this talk we will review the classical homotopy hypothesis, and then focus on the stable version. After discussing what the stable homotopy hypothesis should look like on the categorical side, we will use the Tamsamani model of higher categories to provide a proof. This is based on joint work with Moser, Ozornova, Paoli and Verdugo.

Aktualizováno Středa, 18 Listopad 2020 11:29