Homology, Homotopy and Applications
Volume 16 (2014)
Exact sequences of commutative monoids and semimodules
Pages: 199 – 214
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.
exact sequence, semimodule, semiring, commutative monoid, homological lemma, snake lemma
2010 Mathematics Subject Classification
16Y60, 18A30, 18G60