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Theorems · Theorem · category theory

CategoryTheory.Sheaf.truth_hom

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C),
  (CategoryTheory.Sheaf.truth J).hom = CategoryTheory.Subfunctor.lift (CategoryTheory.Presheaf.truth C) ⋯
Defined in
Mathlib.CategoryTheory.Topos.Sheaf
Cited by
1 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

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

CategoryTheory.Sheaf.χ_unique · cited by 0Sheaf.χ_uniqueCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.Functor.const · cited by 1264Functor.constCategoryTheory.Presheaf.IsSheaf · cited by 991Presheaf.IsSheafCategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homCategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…CategoryTheory.Subfunctor.toFunctor · cited by 90Subfunctor.toFunctorCategoryTheory.Functor.sieves · cited by 20Functor.sievesCategoryTheory.Limits.Types.isTerminalPUnit · cited by 12Types.isTerminalPUnitCategoryTheory.Functor.closedSieves · cited by 11Functor.closedSievesSheaf.truth_homCITED BYCITES

Cites20

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Cited by1

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