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Theorems · Theorem · category theory

CategoryTheory.Over.OverMorphism.ext

∀ {T : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} T] {X : T} {U V : CategoryTheory.Over X} {f g : U ⟶ V},
  CategoryTheory.Over.Hom.left f = CategoryTheory.Over.Hom.left g → f = g
Defined in
Mathlib.CategoryTheory.Comma.Over.Basic
Cited by
27 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

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

AlgebraicGeometry.ext_of_isDominant_of_isSeparated · cited by 3AlgebraicGeometry.ext_of_…CategoryTheory.Over.sectionsUncurry_sectionsCurry · cited by 2Over.sectionsUncurry_sect…CategoryTheory.Sieve.functorPushforward_over_map · cited by 1Sieve.functorPushforward_…AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed · cited by 1AlgebraicGeometry.isCommM…CategoryTheory.CommSq.HasLift.over · cited by 1HasLift.overCategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor · cited by 1Pseudofunctor.isPrestackF…CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor' · cited by 1Pseudofunctor.isPrestackF…CategoryTheory.Sieve.overEquiv_symm_generate · cited by 1Sieve.overEquiv_symm_gene…CategoryTheory.Presieve.isSheafFor_over_map_op_comp_iff · cited by 1Presieve.isSheafFor_over_…CategoryTheory.Presieve.isSheafFor_over_map_op_comp_ofArrows_iff · cited by 1Presieve.isSheafFor_over_…AlgebraicGeometry.Scheme.Cover.overEquiv_generate_toPresieveOver_eq_ofArrows · cited by 1Cover.overEquiv_generate_…CategoryTheory.GrothendieckTopology.overMapPullback_assoc · cited by 1GrothendieckTopology.over…CategoryTheory.GrothendieckTopology.overMapPullback_comp_id · cited by 1GrothendieckTopology.over…CategoryTheory.GrothendieckTopology.overMapPullback_id_comp · cited by 1GrothendieckTopology.over…CategoryTheory.GrothendieckTopology.over_map_compatiblePreserving · cited by 0GrothendieckTopology.over…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitCategoryTheory.Comma.right · cited by 727Comma.rightCategoryTheory.Comma · cited by 566CategoryTheory.CommaCategoryTheory.Over.left · cited by 541Over.leftCategoryTheory.Comma.hom · cited by 490Comma.homCategoryTheory.Over.Hom.left · cited by 287Hom.leftOverMorphism.extCITED BYCITES

Cites15

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Cited by27

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