Presentable categories internal to an infinity-topos


We develop the theory of presentable categories internal to an infinity-topos B. We provide several characterisations of these, including a description in terms of the assoiated sheaves of infinity-categories as well as an internal analogue of the Lurie-Simpson characterisation of presentable infinity-categories. We furthermore establish various structural results about presentable internal categories, such as adjoint functor theorems and a symmetric monoidal structure.

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.