25 citations · 68 across the 12 of their papers we have counts for
14 papers · 1 filter
Cartesian exponentiation and monadicity
Emily Riehl, Dominic Verity
An important result in quasi-category theory due to Lurie is the that cocartesian fibrations are exponentiable, in the sense that pullback along a cocartesian fibration admits a ri…
On the construction of limits and colimits in -categories
Emily Riehl, Dominic Verity
In previous work, we introduce an axiomatic framework within which to prove theorems about many varieties of infinite-dimensional categories simultaneously. In this paper, we estab…
Recognizing quasi-categorical limits and colimits in homotopy coherent nerves
Emily Riehl, Dominic Verity
In this paper we prove that various quasi-categories whose objects are -categories in a very general sense are complete: admitting limits indexed by all simplicial sets. Th…
The comprehension construction
Emily Riehl, Dominic Verity
In this paper we construct an analogue of Lurie's "unstraightening" construction that we refer to as the "comprehension construction". Its input is a cocartesian fibration $p \colo…
Infinity category theory from scratch
Emily Riehl, Dominic Verity
We use the terms "-categories" and "-functors" to mean the objects and morphisms in an "-cosmos." Quasi-categories, Segal categories, complete Segal spaces,…
Kan extensions and the calculus of modules for -categories
Emily Riehl, Dominic Verity
Various models of -categories, including quasi-categories, complete Segal spaces, Segal categories, and naturally marked simplicial sets can be considered as the object…