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Theorems · Definition · category theory

Quiver.Hom.toLoc

{C : Type u} → [inst : CategoryTheory.CategoryStruct.{v, u} C] → {a b : C} → (a ⟶ b) → ({ as := a } ⟶ { as := b })

The 1-morphism in LocallyDiscrete C associated to a given morphism f : a ⟶ b in C

Defined in
Mathlib.CategoryTheory.Bicategory.LocallyDiscrete
Cited by
150 results in Mathlib
Foundations
Depth 4 from the axioms, rests on 12 definitions · uses no axioms
Assumes
CategoryTheory.CategoryStruct

Around this declaration

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

CategoryTheory.Pseudofunctor.DescentData'.pullHom' · cited by 29DescentData'.pullHom'CategoryTheory.Pseudofunctor.DescentData.hom · cited by 28DescentData.homCategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.pullHom · cited by 23LocallyDiscreteOpToCat.pu…CategoryTheory.Pseudofunctor.DescentData'.hom · cited by 22DescentData'.homCategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.hom · cited by 22DescentDataAsCoalgebra.homCategoryTheory.Pseudofunctor.toDescentData · cited by 21Pseudofunctor.toDescentDa…CategoryTheory.Pseudofunctor.DescentData.pullFunctor · cited by 16DescentData.pullFunctorCategoryTheory.Pseudofunctor.presheafHom · cited by 15Pseudofunctor.presheafHomCategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence · cited by 13DescentDataAsCoalgebra.co…CategoryTheory.Pseudofunctor.CoGrothendieck.Hom.fiber · cited by 11Hom.fiberCategoryTheory.Pseudofunctor.Grothendieck.Hom.fiber · cited by 9Hom.fiberCategoryTheory.Pseudofunctor.CoGrothendieck.map · cited by 8CoGrothendieck.mapCategoryTheory.Pseudofunctor.Grothendieck.map · cited by 8Grothendieck.mapCategoryTheory.Pseudofunctor.DescentData'.pullHom'_eq_pullHom · cited by 7DescentData'.pullHom'_eq_…CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebra · cited by 6Pseudofunctor.toDescentDa…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…CategoryTheory.LocallyDiscrete · cited by 318CategoryTheory.LocallyDis…Hom.toLocCITED BYCITES

Cites3

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Cited by218

Results whose statement or proof uses this declaration.