Exactness of short complexes in concrete abelian categories #

If an additive concrete category C has an additive forgetful functor to Ab which preserves homology, then a short complex S in C is exact if and only if it is so after applying the functor forget₂ C Ab.

This lemma allows the computation of the connecting homomorphism D.δ when D : SnakeInput C and C is a concrete category.