Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.opcyclesMap

{C : Type u_1} →
  {ι : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} ι] →
        [inst_2 : CategoryTheory.Abelian C] →
          (X : CategoryTheory.Abelian.SpectralObject C ι) →
            {i j k : ι} →
              (f : i ⟶ j) →
                (g : j ⟶ k) →
                  {i' j' k' : ι} →
                    (f' : i' ⟶ j') →
                      (g' : j' ⟶ k') →
                        (CategoryTheory.ComposableArrows.mk₂ f g ⟶ CategoryTheory.ComposableArrows.mk₂ f' g') →
                          (n : ℤ) → X.opcycles f g n ⟶ X.opcycles f' g' n

The functoriality of X.opcycles with respect to morphisms in ComposableArrows ι 2.

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

22 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian