License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.61
URN: urn:nbn:de:0030-drops-145010
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14501/
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Ikebuchi, Mirai

A Homological Condition on Equational Unifiability

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LIPIcs-MFCS-2021-61.pdf (0.7 MB)

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.

BibTeX - Entry

@InProceedings{ikebuchi:LIPIcs.MFCS.2021.61,
  author =	{Ikebuchi, Mirai},
  title =	{{A Homological Condition on Equational Unifiability}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{61:1--61:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14501},
  URN =		{urn:nbn:de:0030-drops-145010},
  doi =		{10.4230/LIPIcs.MFCS.2021.61},
  annote =	{Keywords: Equational unification, Homological algebra, equational theories}
}

Keywords: Equational unification, Homological algebra, equational theories
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021

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