Theorems · Definition · category theory

CategoryTheory.MorphismProperty.RespectsLeft.casesOn

{C : Type u} →
  [inst : CategoryTheory.CategoryStruct.{v, u} C] →
    {P Q : CategoryTheory.MorphismProperty C} →
      {motive : P.RespectsLeft Q → Sort u_1} →
        (t : P.RespectsLeft Q) →
          ((precomp :
                ∀ {X Y Z : C} (i : X ⟶ Y), Q i → ∀ (f : Y ⟶ Z), P f → P (CategoryTheory.CategoryStruct.comp i f)) →
              motive ⋯) →
            motive t

Defined in: Mathlib.CategoryTheory.MorphismProperty.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: CategoryTheory.CategoryStruct

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Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.CategoryStructstatement and proof · cited by 343
CategoryTheory.MorphismProperty.RespectsLeftstatement and proof · cited by 6

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