Theorems · Theorem · category theory
CategoryTheory.ExtremalEpi.subobject_eq_top
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) [CategoryTheory.ExtremalEpi f]
{A : CategoryTheory.Subobject Y}, A.Factors f → A = ⊤- Defined in
- Mathlib.CategoryTheory.ExtremalEpi
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- Top.topstatement · cited by 9,680
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.arrowproof · cited by 175
- CategoryTheory.Subobject.Factorsstatement and proof · cited by 56
- CategoryTheory.Subobject.factorThruproof · cited by 35
- CategoryTheory.Subobject.factorThru_arrowproof · cited by 31
- CategoryTheory.ExtremalEpistatement and proof · cited by 7
- CategoryTheory.Subobject.isIso_arrow_iff_eq_topproof · cited by 4
- CategoryTheory.ExtremalEpi.isIsoproof · cited by 3
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