Theorems · Theorem · category theory

CategoryTheory.ExtremalEpi.isIso

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {X Y : C} (f : X ⟶ Y) [self : CategoryTheory.ExtremalEpi f]
  {Z : C} (p : X ⟶ Z) (i : Z ⟶ Y),
  CategoryTheory.CategoryStruct.comp p i = f → ∀ [CategoryTheory.Mono i], CategoryTheory.IsIso i

Defined in: Mathlib.CategoryTheory.ExtremalEpi
Cited by: 3 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.ExtremalEpi CategoryTheory.Mono

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Cites6

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.IsIsostatement · cited by 1,156
CategoryTheory.Monostatement · cited by 893
CategoryTheory.ExtremalEpistatement and proof · cited by 7

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.IsStrongGenerator.mk_of_exists_extremalEpiproof · cited by 1
CategoryTheory.extremalEpi_iff_strongEpi_of_hasPullbacksproof · cited by 0
CategoryTheory.ExtremalEpi.subobject_eq_topproof · cited by 0