Theorems · Definition · category theory
CategoryTheory.Over.forget
{T : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} T] → (X : T) → CategoryTheory.Functor (CategoryTheory.Over X) TThe 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.Functor.fromPUnitproof · cited by 769
- CategoryTheory.Comma.fstproof · cited by 76
Cited by219
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.underlyingproof · cited by 211
- CategoryTheory.Subobject.underlyingIsoproof · cited by 41
- CategoryTheory.Sieve.overEquivproof · cited by 28
- CategoryTheory.Presieve.diagramproof · cited by 17
- CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceInversestatement and proof · cited by 10
- CategoryTheory.presheafHomproof · cited by 10
- CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctorstatement · cited by 8
- AlgebraicGeometry.isLimitOpensConeproof · cited by 8
- CategoryTheory.WithTerminal.commaFromOverproof · cited by 7
- CategoryTheory.Over.equivalenceOfIsTerminalproof · cited by 7
- CategoryTheory.forgetAdjToOverstatement · cited by 7
- CategoryTheory.equivToOverUnitproof · cited by 6
Showing the 200 most cited of 219.