Theorems · Definition · category theory

CategoryTheory.Limits.image.preComp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      (f : X ⟶ Y) →
        {Z : C} →
          (g : Y ⟶ Z) →
            [inst_1 : CategoryTheory.Limits.HasImage g] →
              [inst_2 : CategoryTheory.Limits.HasImage (CategoryTheory.CategoryStruct.comp f g)] →
                CategoryTheory.Limits.image (CategoryTheory.CategoryStruct.comp f g) ⟶ CategoryTheory.Limits.image g

The comparison map image (f ≫ g) ⟶ image g.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Images
Cited by: 7 results in Mathlib
Foundations: Depth 10 from the axioms · uses propext, Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasImage CategoryTheory.Limits.HasImage

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

Cites8

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.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Limits.imagestatement and proof · cited by 124
CategoryTheory.Limits.HasImagestatement and proof · cited by 107
CategoryTheory.Limits.image.ιproof · cited by 104
CategoryTheory.Limits.factorThruImageproof · cited by 55
CategoryTheory.Limits.image.liftproof · cited by 16

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.image.preComp_ιstatement · cited by 3
CategoryTheory.Limits.imageSubobject_comp_leproof · cited by 3
CategoryTheory.Limits.imageSubobject_iso_compproof · cited by 2
CategoryTheory.Limits.image.factorThruImage_preCompstatement · cited by 1
CategoryTheory.Limits.image.preComp_compstatement · cited by 0
CategoryTheory.Limits.image.preComp_ι_assocstatement and proof · cited by 0
CategoryTheory.Limits.image.factorThruImage_preComp_assocstatement and proof · cited by 0