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Theorems · Definition · category theory

CategoryTheory.Under.forget

{T : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} T] → (X : T) → CategoryTheory.Functor (CategoryTheory.Under X) T

The forgetful functor mapping an arrow to its domain.

Defined in
Mathlib.CategoryTheory.Comma.Over.Basic
Cited by
90 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom · cited by 24FunctorCategory.HasFuncto…CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom · cited by 23FunctorCategory.functorEn…CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse · cited by 10StructuredArrow.ofCommaSn…CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp · cited by 9FunctorCategory.functorEn…CategoryTheory.StructuredArrow.ofCommaSndEquivalenceFunctor · cited by 8StructuredArrow.ofCommaSn…CategoryTheory.Under.equivalenceOfIsInitial · cited by 7Under.equivalenceOfIsInit…CategoryTheory.WithInitial.commaFromUnder · cited by 7WithInitial.commaFromUnderCategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g · cited by 6injectivity₀.gCategoryTheory.Enriched.FunctorCategory.functorEnrichedId · cited by 6FunctorCategory.functorEn…CategoryTheory.StructuredArrow.ofDiagEquivalence.functor · cited by 6ofDiagEquivalence.functorCategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.functor · cited by 6ofStructuredArrowProjEqui…CategoryTheory.StructuredArrow.ofStructuredArrowProjEquivalence.inverse · cited by 6ofStructuredArrowProjEqui…CategoryTheory.StructuredArrow.ofCommaSndEquivalence · cited by 4StructuredArrow.ofCommaSn…CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse · cited by 4ofDiagEquivalence.inverseCategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.f · cited by 3injectivity₀.fCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitCategoryTheory.Under · cited by 276CategoryTheory.UnderCategoryTheory.Comma.snd · cited by 51Comma.sndUnder.forgetCITED BYCITES

Cites6

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Cited by127

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