Internal languages of locally cartesian closed (∞,1)-categories
Abstract
We establish a DK-equivalence between the relative category of π-tribes and the relative category of locally cartesian closed quasicategories. From this follows one of the internal languages conjecture: Martin-L\"of type theory with dependent sums, intensional identity types, and dependent products satisfying functional extensionality is the internal language of locally cartesian closed (∞,1)-categories.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.