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math.CT2021★ 1 cited
Colimits and cocompletions in internal higher category theory
Louis Martini, Sebastian Wolf
We develop a number of basic concepts in the theory of categories internal to an -topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal…
math.CT2021★ 1 cited
Yoneda's lemma for internal higher categories
Louis Martini
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 G…