Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
In the context of (infinity,1)-category theory, the concept of a double ∞-category plays the same role as that of a double category in ordinary category theory.
A double ∞-category is a 2-dimensional construct that has (a space of) objects and two types of (spaces of) arrows (1-cells) between objects: vertical arrows and horizontal arrows. A double ∞-category also contains (a space of) 2-cells.
Double ∞-categories were introduced in
Other works include:
Lyne Moser, A double (∞,1)-categorical nerve for double categories [arXiv:2007.01848]
Jaco Ruit, Formal category theory in ∞-equipments I [arXiv:2308.03583]
Last revised on March 26, 2025 at 10:10:45. See the history of this page for a list of all contributions to it.