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Online seminář z algebry - 24.6.2021 PDF Tisk

Další seminář z algebry se koná 24.6.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Giulio Lo Monaco

Vopěnka's principle in infinity-categories

Abstrakt:
Vopěnka's principle has arisen as a model theoretical statement, provably independent of ZFC set theory. However, there are a number of categorical ways of formulating it, preventing the existence of proper classes of objects with some conditions in presentable categories, and these are what our attention will be focused on. In particular, we will look at analogous statements in the context of oo-categories and we will ask how these new statements interact with the older ones. Moreover, some of the consequences of Vopěnka's principle on classes of subcategories of presentable categories are investigated and to some extent generalized to oo-categories. A parallel discussion is undertaken about the similar but weaker statement known as weak Vopěnka's principle.

Aktualizováno Úterý, 22 Červen 2021 15:34
 
Online seminář z algebry - 17.6.2021 PDF Tisk

Další seminář z algebry se koná 17.6.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Leonardo Larizza

Lax factorisation systems and categories of partial maps

Abstrakt:
Lax factorisation systems and categories of partial maps
Factorisation systems describe morphisms in a category by factorising them into pairs of composable morphisms. Their definition depends on a  kind of orthogonality relation between morphisms, which entails the existence of some diagonal morphisms for certain squares. In this seminar we present the new notion of lax weak orthogonality between morphisms, which involves lax squares and the factorisation systems it generates. Then we will introduce lax versions of functorial and algebraic weak factorisation systems and some of their properties. These lax factorisation systems are discussed, keeping the theory of ordinary factorisation systems as a blueprint and providing useful properties.
An overview of the examples of such lax factorisation systems is presented in the context of partial maps. We conclude with a discussion of general constructions of these examples and their description in the particular case of sets with partial maps.

Aktualizováno Úterý, 15 Červen 2021 13:52
 
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