Theorems · Theorem · category theory
CategoryTheory.Subobject.isIso_arrow_iff_eq_top
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {Y : C} (P : CategoryTheory.Subobject Y),
CategoryTheory.IsIso P.arrow ↔ P = ⊤- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CategoryTheory.Functor.objstatement · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowstatement and proof · cited by 175
- CategoryTheory.Subobject.isIso_iff_mk_eq_topproof · cited by 6
- CategoryTheory.Subobject.mk_arrowproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isStrongGenerator_iffproof · cited by 5
- CategoryTheory.Subobject.eq_top_of_isIso_arrowproof · cited by 0
- CategoryTheory.ExtremalEpi.subobject_eq_topproof · cited by 0