Abstract
Equational unification is the problem of solving an equation modulo equational axioms. In this paper, we provide a relationship between equational unification and homological algebra for equational theories. We will construct a functor from the category of sets of equational axioms to the category of abelian groups. Then, our main theorem gives a necessary condition of equational unifiability that is described in terms of abelian groups associated with equational axioms and homomorphisms between them. To construct our functor, we use a ringoid (a category enriched over the category of abelian groups) obtained from the equational axioms and a free resolution of a good module over the ringoid, which was developed by Malbos and Mimram.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
