Theorems · Definition · category theory
CategoryTheory.CategoryStruct.comp
{obj : Type u} → [self : CategoryTheory.CategoryStruct.{v, u} obj] → {X Y Z : obj} → (X ⟶ Y) → (Y ⟶ Z) → (X ⟶ Z)Composition of morphisms in a category, written f ≫ g.
- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 17,999 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 5 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStructstatement and proof · cited by 343
Cited by21,717
Results whose statement or proof uses this declaration.
- CategoryTheory.Category.assocstatement · cited by 6,433
- CategoryTheory.Category.comp_idstatement · cited by 2,119
- CategoryTheory.Category.id_compstatement · cited by 1,998
- CategoryTheory.Functor.map_compstatement · cited by 734
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Bicategory.whiskerRightstatement · cited by 531
- CategoryTheory.Bicategory.whiskerLeftstatement · cited by 524
- CategoryTheory.cancel_monostatement and proof · cited by 435
- CategoryTheory.Bicategory.associatorstatement · cited by 405
- CategoryTheory.comp_applystatement · cited by 387
- CategoryTheory.cancel_epistatement and proof · cited by 380
- CategoryTheory.Limits.comp_zerostatement · cited by 365
Showing the 200 most cited of 21,717.