Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Exact sequences of commutative monoids and semimodules

Pages: 199 – 214

DOI: https://dx.doi.org/10.4310/HHA.2014.v16.n1.a12


Jawad Y. Abuhlail (Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia)


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

Published 2 June 2014