Theorems · Theorem · category theory
CategoryTheory.Iso.refl_trans
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (α : X ≅ Y), CategoryTheory.Iso.refl X ≪≫ α = α- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 16 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.
Cites7
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.Iso.homproof · cited by 7,684
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Iso.reflstatement · cited by 727
- CategoryTheory.Iso.transstatement · cited by 566
- CategoryTheory.Iso.extproof · cited by 166
Cited by27
Results whose statement or proof uses this declaration.
- CategoryTheory.ShiftedHom.mk₀_compproof · cited by 13
- CategoryTheory.ShiftedHom.comp_mk₀proof · cited by 11
- CategoryTheory.ShiftedHom.map_mk₀proof · cited by 5
- CategoryTheory.ExactPairing.coevaluation_evaluation''proof · cited by 3
- CategoryTheory.ExactPairing.evaluation_coevaluation''proof · cited by 3
- CategoryTheory.Limits.opParallelPairIso_hom_app_zeroproof · cited by 2
- CategoryTheory.Limits.opParallelPairIso_inv_app_oneproof · cited by 2
- CategoryTheory.Iso.symm_self_id_assocproof · cited by 2
- CategoryTheory.Pseudofunctor.mapComp'_eq_mapCompproof · cited by 2
- CategoryTheory.Limits.opParallelPairIso_hom_app_oneproof · cited by 1