2103.17141Mar 31, 2021Simplified the proof of the Grothendieck construction; removed a flaw in the proof of Yoneda's lemma and spelled out a few lemmas to this proof wich have been left implicit in the previous versions. Changed some terminology and removed typos. Restructured the last part of the paper
Yoneda's lemma for internal higher categories
Louis Martini
Abstract
We develop some basic concepts in the theory of higher categories internal to an arbitrary ∞-topos. We define internal left and right fibrations and prove a version of the Grothendieck construction and of Yoneda's lemma for internal categories.