2 citations · 2 across the 5 of their papers we have counts for
6 papers
The universal coCartesian fibration
Denis-Charles Cisinski, Hoang Kim Nguyen
We give a new proof of the straightening/unstraightening correspondence by proving a generalization of the univalence property of the universal coCartesian fibration.
A note on coCartesian fibrations
Hoang Kim Nguyen
We prove properness of (co)Cartesian fibrations as well as a straightening and unstraightening equivalence, which is compatible with cartesian products, when the base is the nerve…
-type theories
Hoang Kim Nguyen, Taichi Uemura
We introduce -type theories as an -categorical generalization of the categorical definition of type theories introduced by the second named author. We establish ana…
Higher weak (co)limits, adjoint functor theorems, and higher Brown representability
Hoang Kim Nguyen, George Raptis, Christoph Schrade
We prove general adjoint functor theorems for weakly (co)complete -categories. This class of -categories includes the homotopy -categories of (co)complete -categor…
Covariant & Contravariant Homotopy Theories
Hoang Kim Nguyen
Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We s…
Adjoint functor theorems for -categories
Hoang Kim Nguyen, George Raptis, Christoph Schrade
Adjoint functor theorems give necessary and sufficient conditions for a functor to admit an adjoint. In this paper we prove general adjoint functor theorems for functors between $\…