20 citations · 82 across the 18 of their papers we have counts for
4 papers · 1 filter
On the -topos semantics of homotopy type theory
Emily Riehl
Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article…
Identity Types in Algebraic Model Structures and Cubical Sets
Andrew Swan
We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct mann…
W-Types with Reductions and the Small Object Argument
Andrew Swan
We define a simple kind of higher inductive type generalising dependent -types, which we refer to as -types with reductions. Just as dependent -types can be characterised…
Lifting Problems in Grothendieck Fibrations
Andrew Swan
Many interesting classes of maps from homotopical algebra can be characterised as those maps with the right lifting property against certain sets of maps (such classes are sometime…