Theorems · Definition · category theory

CategoryTheory.ShiftedHom.comp

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {M : Type u_4} →
      [inst_1 : AddMonoid M] →
        [inst_2 : CategoryTheory.HasShift C M] →
          {X Y Z : C} →
            {a b c : M} →
              CategoryTheory.ShiftedHom X Y a →
                CategoryTheory.ShiftedHom Y Z b → b + a = c → CategoryTheory.ShiftedHom X Z c

The composition of f : X ⟶ Y⟦a⟧ and g : Y ⟶ Z⟦b⟧, as a morphism X ⟶ Z⟦c⟧ when b + a = c.

Defined in

Mathlib.CategoryTheory.Shift.ShiftedHom

Cited by

54 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShift