Theorems · Definition · category theory

CategoryTheory.ComposableArrows.sc

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {n : ℕ} →
        (S : CategoryTheory.ComposableArrows C n) →
          S.IsComplex →
            (i : ℕ) → autoParam (i + 2 ≤ n) CategoryTheory.ComposableArrows.sc._auto_1 → CategoryTheory.ShortComplex C

The short complex consisting of maps S.map' i (i + 1) and S.map' (i + 1) (i + 2) when we know that S : ComposableArrows C n satisfies S.IsComplex.

Defined in

Mathlib.Algebra.Homology.ExactSequence

Cited by

16 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms