nLab double infinity-category

Contents

Context

(,1)(\infty,1)-Category theory

Homotopy theory

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

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

(,1)(\infty,1)-topos theory

(∞,1)-topos theory

structures in a cohesive (∞,1)-topos

Contents

Idea

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.

References

Double ∞-categories were introduced in

  • Rune Haugseng, Weakly enriched higher categories, Ph.D. thesis, Massachusetts Institute of Technology, 2013.

Other works include:

Last revised on March 26, 2025 at 10:10:45. See the history of this page for a list of all contributions to it.