Theorems · Inductive type · category theory

CategoryTheory.WellPowered

(C : Type u₁) → [inst : CategoryTheory.Category.{v, u₁} C] → [CategoryTheory.LocallySmall.{w, v, u₁} C] → Prop

A category (with morphisms in Type v) is well-powered relative to a universe w if it is locally small and Subobject X is w-small for every X. We show in wellPowered_of_essentiallySmall_monoOver and essentiallySmall_monoOver that this is the case if and only if MonoOver X is w-essentially small for every X.

Defined in

Mathlib.CategoryTheory.Subobject.WellPowered

Cited by

22 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall