Basic homological lemmas well known for modules over rings and, more generally, in the context of abelian categories, have been extended to many other concrete and abstract-categorical contexts by various authors. We propose a new such extension, specifically for commutative monoids and semimodules; these two contexts are equivalent since the forgetful functors from varieties of semimodules to the variety of commutative monoids preserve all limits and colimits.
Homology Homotopy Appl.
16(1):
199-214
(2014).