Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.prop_of_iso
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C)
[P.IsClosedUnderIsomorphisms] {X Y : C} (e : X ≅ Y), P X → P Y- Cited by
- 23 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Isostatement and proof · cited by 3,963
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.ObjectProperty.IsClosedUnderIsomorphismsstatement and proof · cited by 68
- CategoryTheory.ObjectProperty.IsClosedUnderIsomorphisms.of_isoproof · cited by 1
Cited by23
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.prop_iff_of_isoproof · cited by 13
- CategoryTheory.ObjectProperty.isoClosure_eq_selfproof · cited by 12
- CategoryTheory.ObjectProperty.limitsClosure_leproof · cited by 6
- CategoryTheory.ObjectProperty.colimitsClosure_leproof · cited by 6
- CategoryTheory.Triangulated.TStructure.isGE_of_isoproof · cited by 5
- CategoryTheory.ObjectProperty.trW_iff_of_distinguishedproof · cited by 4
- CategoryTheory.Triangulated.TStructure.isLE_of_isoproof · cited by 4
- CategoryTheory.ObjectProperty.shiftClosure_eq_selfproof · cited by 4
- CategoryTheory.ObjectProperty.prop_of_isZeroproof · cited by 3
- AlgebraicGeometry.geometrically_iff_of_isClosedUnderIsomorphismsproof · cited by 3
- CategoryTheory.ObjectProperty.exists_comp_monoModSerre_eq_zero_iffproof · cited by 2
- CategoryTheory.ObjectProperty.exists_epiModSerre_comp_eq_zero_iffproof · cited by 2