# nLab ultracategory

model theory

## Dimension, ranks, forking

• forking and dividing?

• Morley rank?

• Shelah 2-rank?

• Lascar U-rank?

• Vapnik–Chervonenkis dimension?

## Theorems

### Idea

Ultracategories are categories with extra structure, called an ultrastructure (see Lurie, Sec 1.3). They were introduced in Makkai 87 in order to prove conceptual completeness, but note that Lurie’s definition differs from Makkai’s (Lurie, Warning 1.0.4).

### References

Last revised on January 8, 2019 at 09:03:18. See the history of this page for a list of all contributions to it.