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Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.Hom.hom

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} → {Φ₁ Φ₂ : J.Point} → Φ₁.Hom Φ₂ → (Φ₂.fiber ⟶ Φ₁.fiber)

a natural transformation, in the opposite direction

Defined in
Mathlib.CategoryTheory.Sites.Point.Category
Cited by
12 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber · cited by 4Hom.presheafFiberCategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_app · cited by 3Hom.presheafFiber_appCategoryTheory.GrothendieckTopology.Point.Hom.ext · cited by 2Hom.extCategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp · cited by 2Hom.presheafFiber_compCategoryTheory.GrothendieckTopology.Point.comp_hom · cited by 1Point.comp_homCategoryTheory.GrothendieckTopology.Point.hom_ext · cited by 1Point.hom_extCategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_id · cited by 1Hom.presheafFiber_idCategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_comp · cited by 1Hom.sheafFiber_compCategoryTheory.GrothendieckTopology.pointBotFunctor_map_hom · cited by 0GrothendieckTopology.poin…CategoryTheory.GrothendieckTopology.Point.comp_hom_assoc · cited by 0Point.comp_hom_assocCategoryTheory.GrothendieckTopology.Point.hom_ext_iff · cited by 0Point.hom_ext_iffCategoryTheory.GrothendieckTopology.Point.id_hom · cited by 0Point.id_homCategoryTheory.GrothendieckTopology.Point.Hom.ext_iff · cited by 0Hom.ext_iffCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.GrothendieckTopology.Point · cited by 123GrothendieckTopology.PointCategoryTheory.GrothendieckTopology.Point.fiber · cited by 93Point.fiberCategoryTheory.GrothendieckTopology.Point.Hom · cited by 5Point.HomHom.homCITED BYCITES

Cites7

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Cited by13

Results whose statement or proof uses this declaration.