Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.id_mem
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (W : CategoryTheory.MorphismProperty C) [W.ContainsIdentities]
(X : C), W (CategoryTheory.CategoryStruct.id X)- Cited by
- 23 results in Mathlib
- Foundations
- Depth 5 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.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.ContainsIdentitiesstatement and proof · cited by 94
- CategoryTheory.MorphismProperty.ContainsIdentities.id_memproof · cited by 4
Cited by29
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.LeftFraction.ofHomproof · cited by 8
- CategoryTheory.MorphismProperty.of_isIsoproof · cited by 5
- CategoryTheory.MorphismProperty.RightFraction.ofHomproof · cited by 5
- AlgebraicGeometry.IsZariskiLocalAtSource.of_isOpenImmersionproof · cited by 5
- CategoryTheory.MorphismProperty.overEquivOfIsInitialproof · cited by 4
- CategoryTheory.MorphismProperty.underEquivOfIsTerminalproof · cited by 4
- CategoryTheory.MorphismProperty.multiplicativeClosure_le_iffproof · cited by 4
- SimplexCategory.Truncated.morphismProperty_eq_topproof · cited by 2
- CategoryTheory.MorphismProperty.composePath_memproof · cited by 2
- SimplexCategoryGenRel.multiplicativeClosure_isGenerator_eq_topproof · cited by 2
- HomotopicalAlgebra.ReedyStructure.degHom_idproof · cited by 2
- CategoryTheory.MorphismProperty.IsMonoidal.mk'proof · cited by 1