Ehresmann monoids : Adequacy and expansions
| Autor: | Yan Hui Wang, Gracinda M. S. Gomes, Victoria Gould, Mário J. J. Branco |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Monoid
Pure mathematics Algebra and Number Theory 010102 general mathematics 05 social sciences Semilattice 01 natural sciences Mathematics::Category Theory Free monoid 0502 economics and business Mathematics::Differential Geometry 050207 economics 0101 mathematics Initial and terminal objects Mathematics |
| ISSN: | 1090-266X |
| Popis: | 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. Fixing 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. |
| Databáze: | OpenAIRE |
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