Theorems · Definition · category theory
CategoryTheory.InducedCategory.Hom.hom
{C : Type u₁} →
{D : Type u₂} →
[inst : CategoryTheory.Category.{v, u₂} D] →
{F : C → D} → {X Y : CategoryTheory.InducedCategory D F} → X.Hom Y → (F X ⟶ F Y)The underlying morphism.
- Defined in
- Mathlib.CategoryTheory.InducedCategory
- Cited by
- 850 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.InducedCategorystatement and proof · cited by 71
- CategoryTheory.InducedCategory.Homstatement and proof · cited by 12
Cited by988
Results whose statement or proof uses this declaration.
- SheafOfModules.pushforwardproof · cited by 45
- AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMapproof · cited by 34
- CategoryTheory.Functor.mapGrpproof · cited by 32
- CategoryTheory.ObjectProperty.hom_extstatement and proof · cited by 27
- CategoryTheory.Functor.mapAddGrpproof · cited by 27
- CategoryTheory.Functor.mapCommMonproof · cited by 27
- CategoryTheory.Functor.mapCommGrpproof · cited by 25
- AlgebraicGeometry.SheafedSpace.IsOpenImmersionproof · cited by 23
- HomotopicalAlgebra.BifibrantObject.homRelproof · cited by 22
- HomotopicalAlgebra.CofibrantObject.homRelproof · cited by 20
- CategoryTheory.sheafifyLiftproof · cited by 18
- CategoryTheory.InducedCategory.hom_extstatement and proof · cited by 16
Showing the 200 most cited of 988.