nLab
weak omega-category

Weak $\omega$-categories are examples of higher categories, with essentially the same meaning as $\mathrm{\infty }$-categories. The distinction between the terms ”$\omega$-category” and ”$\mathrm{\infty }$-category” is mostly a matter of the preference of individual authors. One slight difference is that $\mathrm{\infty }$-category usually seems to imply a “weak” notion, while in addition to weak $\omega$-categories there are also strict ones.

Examples

• Trimble ∞-category
• simplicial weak ω-category
• Batanin ω-category

References

See the general references at higher category theory.

• André Joyal, Tim Porter, Peter May, Weak categories (pdf)