Theorems · Theorem · category theory
CategoryTheory.Discrete.functor_map_id
∀ {J : Type v₁} {C : Type u₂} [inst : CategoryTheory.Category.{v₂, u₂} C]
(F : CategoryTheory.Functor (CategoryTheory.Discrete J) C) {j : CategoryTheory.Discrete J} (f : j ⟶ j),
F.map f = CategoryTheory.CategoryStruct.id (F.obj j)- Defined in
- Mathlib.CategoryTheory.Discrete.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Discretestatement and proof · cited by 2,447
- CategoryTheory.Functor.map_idproof · cited by 616
Cited by36
Results whose statement or proof uses this declaration.
- CategoryTheory.NatTrans.Equifibered.of_discreteproof · cited by 11
- CategoryTheory.FinitaryExtensive.vanKampenproof · cited by 5
- CategoryTheory.BinaryCofan.isVanKampen_iffproof · cited by 2
- CategoryTheory.isUniversalColimit_extendCofanproof · cited by 2
- CategoryTheory.isVanKampenColimit_extendCofanproof · cited by 1
- AlgebraicGeometry.sigmaι_eq_iffproof · cited by 1
- CategoryTheory.MorphismProperty.le_colimitsOfShape_punitproof · cited by 1
- CategoryTheory.FinitaryExtensive.isVanKampen_finiteCoproducts_Finproof · cited by 1
- CategoryTheory.mono_of_cofan_isVanKampenproof · cited by 1
- CategoryTheory.isPullback_initial_to_of_cofan_isVanKampenproof · cited by 1