nLab
weak omega-category

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

In higher category theory the term weak ω\omega-categories is essentially synonymous with infinity-category in the fully general sense of (infinity,infinity)-category. The terms “ω\omega-category” and “\infty-category” originate in different schools and their choice of use is mostly a matter of the preference of individual authors.

One slight difference is that “\infty-category” usually implies a “weak” (fully general) notion, while in addition to weak ω\omega-categories there are also strict ones. Another difference is that definitions of weak ω\omega-categories tend to be algebraic instead of geometric (accordingly typically the central open question is whether a definition really satisfies the homotopy hypothesis), though some definitions of weak ω\omega-categories are geometry (for instance some flavors of definition of opetopic omega-category).

Examples

The following are examples for proposals of definitions of weak ω\omega-categories.

References

See the general references at higher category theory.

Revised on November 10, 2014 11:28:24 by Urs Schreiber (89.204.155.35)