Factorization systems describe morphisms in a category by factorizing 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 factorization systems it generates. Then we will introduce lax versions of functorial and algebraic weak factorization systems and some of their properties. These lax factorization systems are discussed, keeping the theory of ordinary factorization systems as a blueprint and providing useful properties. An overview of the examples of such lax factorization 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.
This video is part of Masaryk University‘s Algebra seminar.
