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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.

CategoryTheory.ShiftedHom.mk₀_comp · cited by 13ShiftedHom.mk₀_compCategoryTheory.ShiftedHom.comp_mk₀ · cited by 11ShiftedHom.comp_mk₀CategoryTheory.ShiftedHom.map_mk₀ · cited by 5ShiftedHom.map_mk₀CategoryTheory.ExactPairing.coevaluation_evaluation'' · cited by 3ExactPairing.coevaluation…CategoryTheory.ExactPairing.evaluation_coevaluation'' · cited by 3ExactPairing.evaluation_c…CategoryTheory.Limits.opParallelPairIso_hom_app_zero · cited by 2Limits.opParallelPairIso_…CategoryTheory.Limits.opParallelPairIso_inv_app_one · cited by 2Limits.opParallelPairIso_…CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom · cited by 2Pseudofunctor.mapComp'₀₁₃…CategoryTheory.Functor.mapDerivedCategoryFactors_inv_app_mapDerivedCategorySingleFunctor_hom_app · cited by 2Functor.mapDerivedCategor…CategoryTheory.Iso.symm_self_id_assoc · cited by 2Iso.symm_self_id_assocCategoryTheory.Pseudofunctor.mapComp'_eq_mapComp · cited by 2Pseudofunctor.mapComp'_eq…CategoryTheory.Limits.opParallelPairIso_hom_app_one · cited by 1Limits.opParallelPairIso_…CategoryTheory.Iso.self_symm_id_assoc · cited by 1Iso.self_symm_id_assocCategoryTheory.Limits.opParallelPairIso_inv_app_zero · cited by 1Limits.opParallelPairIso_…CategoryTheory.Functor.mapDerivedCategorySingleFunctor_inv_app_mapDerivedCategoryFactors_hom_app · cited by 1Functor.mapDerivedCategor…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.Iso.trans · cited by 566Iso.transCategoryTheory.Iso.ext · cited by 166Iso.extIso.refl_transCITED BYCITES

Cites7

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Cited by27

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