Theorems · Inductive type · category theory

CategoryTheory.ShortComplex.SnakeInput

(C : Type u_1) → [inst : CategoryTheory.Category.{v_1, u_1} C] → [CategoryTheory.Abelian C] → Type (max u_1 v_1)

A snake input in an abelian category C consists of morphisms of short complexes L₀ ⟶ L₁ ⟶ L₂ ⟶ L₃ (which should be visualized vertically) such that L₀ and L₃ are respectively the kernel and the cokernel of L₁ ⟶ L₂, L₁ and L₂ are exact, L₁.g is epi and L₂.f is mono.

Defined in

Mathlib.Algebra.Homology.ShortComplex.SnakeLemma

Cited by

129 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 3 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian