Theorems · Theorem · category theory
CategoryTheory.SmallObject.objMap_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (I : CategoryTheory.MorphismProperty C) (κ : Cardinal.{w})
[inst_1 : Fact κ.IsRegular] [inst_2 : OrderBot κ.ord.ToType] [inst_3 : I.IsCardinalForSmallObjectArgument κ]
{f g h : CategoryTheory.Arrow C} (φ : f ⟶ g) (ψ : g ⟶ h),
CategoryTheory.SmallObject.objMap I κ (CategoryTheory.CategoryStruct.comp φ ψ) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.SmallObject.objMap I κ φ)
(CategoryTheory.SmallObject.objMap I κ ψ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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 and proof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- Factstatement and proof · cited by 2,726
- Cardinalstatement and proof · cited by 2,598
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- OrderBotstatement and proof · cited by 1,055
- CategoryTheory.Functor.map_compproof · cited by 734
- CategoryTheory.Arrowstatement and proof · cited by 713
- CategoryTheory.Arrow.leftstatement · cited by 426
- CategoryTheory.Arrow.rightstatement · cited by 423
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.SmallObject.objMap_comp_assocproof · cited by 0