Theorems · Theorem · category theory

CategoryTheory.Precoverage.ZeroHypercover.restrictIndexOfSmall_toPreZeroHypercover

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Precoverage C} {S : C}
  (E : J.ZeroHypercover S) [inst_1 : E.Small],
  E.restrictIndexOfSmall.toPreZeroHypercover =
    E.restrictIndex (CategoryTheory.Precoverage.ZeroHypercover.Small.restrictFun E)

Defined in: Mathlib.CategoryTheory.Sites.Hypercover.Zero
Cited by: 1 results in Mathlib
Foundations: Depth 14 from the axioms · uses Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Precoverage.ZeroHypercover.Small

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
CategoryTheory.PreZeroHypercoverstatement · cited by 256
CategoryTheory.Precoveragestatement and proof · cited by 204
CategoryTheory.Precoverage.ZeroHypercoverstatement and proof · cited by 81
CategoryTheory.PreZeroHypercover.restrictIndexstatement · cited by 11
CategoryTheory.Precoverage.ZeroHypercover.Small.restrictFunstatement · cited by 8
CategoryTheory.Precoverage.ZeroHypercover.restrictIndexOfSmallstatement and proof · cited by 8
CategoryTheory.Precoverage.ZeroHypercover.Smallstatement and proof · cited by 7
CategoryTheory.Precoverage.ZeroHypercover.Small.Indexstatement · cited by 4

Cited by1

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CategoryTheory.Precoverage.isSheaf_toGrothendieck_iff_of_isStableUnderBaseChange_of_smallproof · cited by 1