Theorems · Definition · category theory

CategoryTheory.Equalizer.Sieve.secondMap

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (P : CategoryTheory.Functor Cᵒᵖ (Type (max v u))) →
      {X : C} →
        (S : CategoryTheory.Sieve X) →
          CategoryTheory.Equalizer.FirstObj P S.arrows ⟶ CategoryTheory.Equalizer.Sieve.SecondObj P S

The map a of Equations (3,4) [MM92].

Defined in: Mathlib.CategoryTheory.Sites.EqualizerSheafCondition
Cited by: 3 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites14

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 and proof · cited by 32,603
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapproof · cited by 8,698
Oppositestatement and proof · cited by 8,081
Quiver.Hom.opproof · cited by 1,948
CategoryTheory.Sievestatement and proof · cited by 552
CategoryTheory.Sieve.arrowsstatement and proof · cited by 446
CategoryTheory.Limits.Pi.πproof · cited by 184
CategoryTheory.Limits.Pi.liftproof · cited by 53

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Equalizer.Sieve.wstatement and proof · cited by 1
CategoryTheory.Equalizer.Sieve.compatible_iffstatement and proof · cited by 0
CategoryTheory.Equalizer.Sieve.equalizer_sheaf_conditionstatement · cited by 0