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Theorems · Definition · category theory

CategoryTheory.Over.forget

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

The forgetful functor mapping an arrow to its domain.

Defined in
Mathlib.CategoryTheory.Comma.Over.Basic
Cited by
164 results in Mathlib
Foundations
Depth 27 from the axioms, rests on 135 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.Subobject.underlying · cited by 211Subobject.underlyingCategoryTheory.Subobject.underlyingIso · cited by 41Subobject.underlyingIsoCategoryTheory.Sieve.overEquiv · cited by 28Sieve.overEquivCategoryTheory.Presieve.diagram · cited by 17Presieve.diagramCategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInverse · cited by 10CostructuredArrow.ofComma…CategoryTheory.presheafHom · cited by 10CategoryTheory.presheafHomCategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor · cited by 8CostructuredArrow.ofComma…AlgebraicGeometry.isLimitOpensCone · cited by 8AlgebraicGeometry.isLimit…CategoryTheory.WithTerminal.commaFromOver · cited by 7WithTerminal.commaFromOverCategoryTheory.Over.equivalenceOfIsTerminal · cited by 7Over.equivalenceOfIsTermi…CategoryTheory.forgetAdjToOver · cited by 7CategoryTheory.forgetAdjT…CategoryTheory.equivToOverUnit · cited by 6CategoryTheory.equivToOve…CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor · cited by 6ofCostructuredArrowProjEq…CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse · cited by 6ofCostructuredArrowProjEq…CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor · cited by 6ofDiagEquivalence.functorCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitCategoryTheory.Comma.fst · cited by 76Comma.fstOver.forgetCITED BYCITES

Cites6

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

Cited by219

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 219.