homological algebra
and
nonabelian homological algebra
additive and abelian categories
additive category
abelian category
semi-abelian category
kernel, cokernel
complex
differential
homology
chain complex
exact sequence, split exact sequence
injective object, projective object
derived category
derived functor
triangulated category
stable (∞,1)-category
A-∞-category
differential graded category
Koszul-Tate resolution
BRST-BV complex
five lemma
snake lemma
Dold-Kan correspondence / monoidal, operadic
Eilenberg-Zilber theorem
universal coefficient theorem
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For now, see http://secure.wikimedia.org/wikipedia/en/wiki/Snake_lemma.