Mathlib Map

Theorems · Inductive type · category theory

CategoryTheory.IsNormalEpiCategory

(C : Type u₁) → [inst : CategoryTheory.Category.{v₁, u₁} C] → [CategoryTheory.Limits.HasZeroMorphisms C] → Prop

A normal epi category is a category in which every epimorphism is normal.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic
Cited by
9 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.ObjectProperty.SerreClassLocalization.abelian · cited by 6SerreClassLocalization.ab…CategoryTheory.normalEpiOfEpi · cited by 3CategoryTheory.normalEpiO…CategoryTheory.NormalEpiCategory.mono_of_zero_kernel · cited by 2NormalEpiCategory.mono_of…CategoryTheory.NormalEpiCategory.preservesMonomorphisms_of_preservesKernels · cited by 1NormalEpiCategory.preserv…CategoryTheory.NonPreadditiveAbelian.casesOn · cited by 0NonPreadditiveAbelian.cas…CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.isNormalEpiCategory · cited by 0OfCoimageImageComparisonI…CategoryTheory.ObjectProperty.preservesMonomorphisms_ι_of_isNormalEpiCategory · cited by 0ObjectProperty.preservesM…CategoryTheory.NonPreadditiveAbelian.mk.noConfusion · cited by 0mk.noConfusionCategoryTheory.NonPreadditiveAbelian.noConfusion · cited by 0NonPreadditiveAbelian.noC…CategoryTheory.NonPreadditiveAbelian.noConfusionType · cited by 0NonPreadditiveAbelian.noC…CategoryTheory.NonPreadditiveAbelian.recOn · cited by 0NonPreadditiveAbelian.rec…CategoryTheory.Abelian.noConfusion · cited by 0Abelian.noConfusionCategoryTheory.Abelian.noConfusionType · cited by 0Abelian.noConfusionTypeCategoryTheory.Abelian.casesOn · cited by 0Abelian.casesOnCategoryTheory.ObjectProperty.SerreClassLocalization.isNormalEpiCategory · cited by 0SerreClassLocalization.is…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.IsNormalEpiCat…CITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by23

Results whose statement or proof uses this declaration.