Theorems · Definition · category theory

CategoryTheory.DifferentialObject.Hom.comp

{S : Type u_1} →
  [inst : AddMonoidWithOne S] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          [inst_3 : CategoryTheory.HasShift C S] →
            {X Y Z : CategoryTheory.DifferentialObject S C} → X.Hom Y → Y.Hom Z → X.Hom Z

The composition of morphisms of differential objects.

Defined in: Mathlib.CategoryTheory.DifferentialObject
Cited by: 1 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddMonoidWithOne CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.HasShift

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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
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.HasShiftstatement and proof · cited by 1,527
AddMonoidWithOnestatement and proof · cited by 313
CategoryTheory.DifferentialObjectstatement and proof · cited by 61
CategoryTheory.DifferentialObject.Hom.fproof · cited by 28
CategoryTheory.DifferentialObject.Homstatement and proof · cited by 9

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.DifferentialObject.Hom.comp_fstatement and proof · cited by 0