Mathlib Map

Theorems · Theorem · category theory

Quiver.Hom.op_inj

∀ {C : Type u₁} [inst : Quiver C] {X Y : C}, Function.Injective Quiver.Hom.op
Defined in
Mathlib.CategoryTheory.Opposites
Cited by
45 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
Quiver

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.toSpecΓ_appTop · cited by 7Scheme.toSpecΓ_appTopCategoryTheory.Limits.IsZero.unop · cited by 5IsZero.unopCategoryTheory.Localization.exists_rightFraction · cited by 5Localization.exists_right…CategoryTheory.Functor.initial_iff_of_isCofiltered · cited by 5Functor.initial_iff_of_is…CategoryTheory.MorphismProperty.LeftFractionRel.unop · cited by 4LeftFractionRel.unopAlgebraicGeometry.Spec.map_inj · cited by 3Spec.map_injCategoryTheory.ObjectProperty.isCoseparating_op_iff · cited by 3ObjectProperty.isCosepara…CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv · cited by 2Pretriangulated.opShiftFu…CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop · cited by 2Functor.map_opShiftFuncto…CategoryTheory.Limits.desc_op_comp_opCoproductIsoProduct'_hom · cited by 2Limits.desc_op_comp_opCop…CategoryTheory.isIso_of_op · cited by 2CategoryTheory.isIso_of_opCategoryTheory.ObjectProperty.isCodetecting_op_iff · cited by 2ObjectProperty.isCodetect…CategoryTheory.ObjectProperty.isDetecting_op_iff · cited by 2ObjectProperty.isDetectin…CategoryTheory.ObjectProperty.isSeparating_op_iff · cited by 2ObjectProperty.isSeparati…CategoryTheory.MorphismProperty.RightFractionRel.unop · cited by 1RightFractionRel.unopQuiver.Hom · cited by 32603Quiver.HomOpposite · cited by 8081OppositeQuiver.Hom.op · cited by 1948Hom.opQuiver.Hom.unop · cited by 903Hom.unopQuiver · cited by 405QuiverHom.op_injCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by45

Results whose statement or proof uses this declaration.