Theorems · Definition · category theory
CategoryTheory.Abelian.app
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → {P Q : C} → (P ⟶ Q) → CategoryTheory.Over P → CategoryTheory.Over QThis is just composition of morphisms in C. Another way to express this would be
(Over.map f).obj a, but our definition has nicer definitional properties.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.compproof · cited by 17,999
- CategoryTheory.Overstatement and proof · cited by 935
- CategoryTheory.Over.homproof · cited by 370
- CategoryTheory.Over.mkproof · cited by 203
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Pseudoelement.pseudoApplyproof · cited by 18
- CategoryTheory.Abelian.app_homstatement · cited by 1
- CategoryTheory.Abelian.Pseudoelement.pseudoApply_auxstatement and proof · cited by 0
- CategoryTheory.Abelian.Pseudoelement.pseudo_exact_of_exactproof · cited by 0
- CategoryTheory.Abelian.Pseudoelement.pseudo_pullbackproof · cited by 0
- CategoryTheory.Abelian.Pseudoelement.pseudo_surjective_of_epiproof · cited by 0
- CategoryTheory.Abelian.Pseudoelement.sub_of_eq_imageproof · cited by 0
- CategoryTheory.Abelian.Pseudoelement.exact_of_pseudo_exactproof · cited by 0