Pereira Fatelo, JorgeMartins-Ferreira, Nelson2025-06-162025-06-162016-09-12Jorge Pereira Fatelo, Nelson Martins-Ferreira, Internal monoids and groups in the category of commutative cancellative medial magmas. Port. Math. 73 (2016), no. 3, pp. 219–245 DOI 10.4171/PM/19860032-51551662-2758http://hdl.handle.net/10400.8/13266This article considers the category of commutative medial magmas with cancellation, a structure that generalizes midpoint algebras and commutative semigroups with cancellation. In this category each object admits at most one internal monoid structure for any given unit. Conditions for the existence of internal monoids and internal groups, as well as conditions under which an internal reflexive relation is a congruence, are studied.engMidpoint algebraCommutative monoidAbelian groupCancellation lawMedial lawQuasigroupInternal monoidInternal groupInternal relationWeakly Mal’tsev categoryjournal article10.4171/pm/1986