Theorems · Theorem · category theory

CategoryTheory.section_comp_left_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A B : C} (f g : A ⟶ B)
  [inst_1 : CategoryTheory.IsReflexivePair f g] {Z : C} (h : B ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.commonSection f g) (CategoryTheory.CategoryStruct.comp f h) = h

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Cited by: 0 results in Mathlib
Foundations: Depth 11 from the axioms · uses Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsReflexivePair

Mathlib docs Source Loogle LeanSearch

Around this declaration

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 · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.IsReflexivePairstatement and proof · cited by 19
CategoryTheory.commonSectionstatement and proof · cited by 7
CategoryTheory.section_comp_leftproof · cited by 3

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.