Poloids from the Points of View of Partial Transformations and Category Theory

2017/10/12 by Dan Jönsson, Dan Jonsson, Jonsson, Dan · 2 citations
Mathematics · #1802 #Algebra over a field #Category Theory (math.CT) #FOS: Mathematics #History and Theory of Mathematics #Mathematics #Mathematics and Applications #Pure mathematics #math.CT #msc:1802

paper · pdf · doi:10.48550/arxiv.1710.04634

published in arXiv (Cornell University) (Cornell University) · 15 pages. Appendix A expanded; minor corrections

openalex publication_date 2017/10/12 · openalex created_date 2017/10/20 · arxiv created 2018/08/03 · arxiv updated 2018/08/06 · openalex updated_date 2026/07/28

Abstract

Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are considered from these two points of view.

Citations

• �ber eine Verallgemeinerung des Gruppenbegriffes

Cited by

• Split Lemma and First Isomorphism Theorem for groupoids

Related

• On free products and amalgams of pomonoids
• On Group-Like Magmoids
• Paracategories I: internal parategories and saturated partial algebras
• Operad of posets 101: The Wixárika posets
• Two partial monoid structures on a set