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

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