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 Online seminář z algebry - 6.5.2021

Další seminář z algebry se koná 6.5.2021 vyjimečně od 14.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

#### Walter Tholen

Spaces vs Categories, Perfect Maps vs Discrete Cofibrations

Abstrakt:
We consider perfect maps of topological spaces and discrete cofibrations of categories to guide us into Burroni's notions of T-category and T-functor. In that environment we establish a so-called comprehensive factorization system that entails the classical Street-Walters system, as well as the (antiperfect, perfect)-system for continuous maps of Tychonoff spaces known since the 1960s.

(Based on joint work with Leila Yeganeh)

Aktualizováno Úterý, 04 Květen 2021 10:05

 Online seminář z algebry - 29.4.2021

Další seminář z algebry se koná 29.4.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

#### Hoang Kim Nguyen

Contravariant Homotopy Theories and Quillen’s Theorem A

Abstrakt:
In this talk I will show how to construct a model structure on a locally presentable category with a suitable cylinder object such that the model structure behaves in a ”covariant” or ”contravariant” way with respect to the cylinder. Examples of such model structures include the covariant and contravariant model structures on simplicial sets and the cocartesian and cartesian model structures on marked simplicial sets modelling presheaves with values in ∞-groupoids and ∞-categories respectively.

The model structures come with an abstract notion of cofinal functor which recovers the usual definition of cofinal functor for ∞-categories when applied to the covariant and contravariant model structures on simplicial sets. When applied to presheaves valued in n-types, one obtains a version of Quillen’s Theorem A for n-categories.

Aktualizováno Pátek, 23 Duben 2021 08:21

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