BIBLIOS

Document type
Journal articles

Document subtype
Full paper

Title
Ehresmann monoids: Adequacy and expansions

Participants in the publication
Mário J.J. Branco (Author)
Dep. Matemática
CEMAT
Gracinda M. S. Gomes (Author)
Dep. Matemática
CEMAT
Victoria Gould (Author)
Yanhui Wang (Author)

Summary
It is known that an Ehresmann monoid P(T,Y) may be constructed from a monoid T acting via order-preserving maps on both sides of a semilattice Y with identity, such that the actions satisfy an appropriate compatibility criterion. Our main result shows that if T is cancellative and equidivisible (as is the case for the free monoid X?), the monoid P(T,Y) not only is Ehresmann but also satisfies the stronger property of being adequate.\n\nFixing T, Y and the actions, we characterise P(T,Y) as being unique in the sense that it is the initial object in a suitable category of Ehresmann monoids. We also prove that the operator P defines an expansion of Ehresmann monoids.


Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Where published
Journal of Algebra

Publication Identifiers
ISSN - 0021-8693

Publisher
Elsevier BV



Document Identifiers
URL - http://dx.doi.org/10.1016/j.jalgebra.2018.06.036
DOI - https://doi.org/10.1016/j.jalgebra.2018.06.036

Rankings
SCIMAGO Q1 (2018) - 1.137 - Algebra and Number Theory
SCIMAGO Q1 (2017) - 1.187 - Algebra and Number Theory