# nLab weak omega-category

### Context

#### Higher category theory

higher category theory

# Contents

## Idea

In higher category theory the term weak $\omega$-categories is essentially synonymous with infinity-category in the fully general sense of (infinity,infinity)-category. The terms “$\omega$-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 $\omega$-categories there are also strict ones. Another difference is that definitions of weak $\omega$-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 $\omega$-categories are geometry (for instance some flavors of definition of opetopic omega-category).

## Examples

The following are examples for proposals of definitions of weak $\omega$-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)