Limits and colimits in internal higher category theory


We develop a number of basic concepts in the theory of categories internal to an infinity-topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal categories, and we use these results to prove the universal property of internal presheaf categories. We furthermore construct the free cocompletion of an internal category by colimits that are indexed by an arbitrary class of diagram shapes.

ArXiv preprint
Louis Martini
Louis Martini
PhD fellow in mathematics

I am a fourth year PhD student in the Department of Mathematical Sciences at the Norwegian University of Science and Technology in Trondheim, Norway.