nLab
class-locally presentable category

Contents

Context

Category theory

Limits and colimits

Contents

Idea

The notion of a class-locally presentable category is a generalisation of that of a locally presentable category: In a class-locally presentable category one may need a proper class of objects (instead of just a small set) to build all the others by suitable colimits.

Definition

Let λ\lambda be a regular cardinal, and let the category CC be complete and cocomplete. Then CC is called class λ\lambda-presentable if there is a class ACA \subset C of λ\lambda-presentable objects such that every object of CC is a λ\lambda-filtered colimit of objects in AA. A category is class-locally presentable if it is class λ\lambda-presentable for some λ\lambda.

If CC merely has λ\lambda-filtered colimits, rather than all colimits (and limits), then it is called class λ\lambda-accessible, and class-accessible if it is class λ\lambda-accessible for some λ\lambda.

  • macrotopos?

References

Last revised on May 4, 2020 at 01:45:04. See the history of this page for a list of all contributions to it.