Kishan DAYARAM (Stellenbosch University) and Luca MESITI (Stellenbosch University) will give talks, respectively, on
Formal analysis of Yoneda-Quillen exact categories
Abstract:
See the attached PDF.
and
Double orthogonal factorization systems
Abstract:
We will present a generalization of the fundamental notion of orthogonal factorization system to the setting of double categories. No knowledge of double category theory will be required, and the talk will be full of examples!
We will see that a double orthogonal factorization system consists of two compatible orthogonal factorisation systems: one for the arrows of the double category and one for the double cells. We will prove that, exactly as ordinary orthogonal factorization systems are algebras for a 2-monad on the 2-category of categories, double orthogonal factorization systems are algebras for a 2-monad on the 2-category of double categories. Interestingly, we reach this result by proving a general monadicity theorem, which guarantees that (under mild conditions) the operation of taking algebras for a monad commutes with that of taking internal categories.
This talk is based on a joint work with Aberle’, Caviglia, Kukla, Maldonado, Pronk and Ralaivaosaona, born as a project for the Adjoint School 2024.