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Theorems · Theorem · category theory

CategoryTheory.HomRel.IsStableUnderPrecomp.comp_left

∀ {C : Type u_1} {inst : CategoryTheory.Category.{v_1, u_1} C} {r : HomRel C}
  [self : CategoryTheory.HomRel.IsStableUnderPrecomp r] {X Y Z : C} (f : X ⟶ Y) {g g' : Y ⟶ Z},
  r g g' → r (CategoryTheory.CategoryStruct.comp f g) (CategoryTheory.CategoryStruct.comp f g')
Defined in
Mathlib.CategoryTheory.Quotient
Cited by
1 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.HomRel.IsStableUnderPrecomp
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Around this declaration

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CategoryTheory.HomRel.compClosure_iff_self · cited by 0HomRel.compClosure_iff_se…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compHomRel · cited by 49HomRelCategoryTheory.HomRel.IsStableUnderPrecomp · cited by 7HomRel.IsStableUnderPreco…IsStableUnderPrecomp.comp_leftCITED BYCITES

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Cited by1

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