A dg category is a category whose Hom-sets carry the structure of
complexes of modules. It is widely used in algebraic geometry and
representation theory as an enhancement of triangulated categories,
providing a richer underlying structure.
Originating from the homotopy theory of complexes up to
quasi-isomorphism, dg categories themselves admit a natural
homotopical structure, whose theoretical foundations have been
extensively developed since the 2000s.

In this talk, I will present an approach to the homotopy theory of dg
categories from the viewpoint of formal category theory --- a
2-categorical framework that seeks to formalise and axiomatise
"category theory" itself by abstracting the structures and phenomena
observed in the 2-category of categories.
I will first outline the basic ideas of formal category theory, and
then explain how these ideas can be applied to the homotopy theory of
dg categories.
16:15 - Tea