Ordered Ehresmann semigroups and categories

Ordered Categories and Ordered Semigroups

Ordered categories and ordered semigroups

We use ordered categories to study semidirect decompositions of finite ordered semigroups. We obtain ordered analogues of the derived category theorem and of the delay theorem. Next we prove that the ordered analogues of semilattices and of J -trivial monoids constitute local varieties, and we derive some decomposition theorems from these results. In [10], Pin and Weil initiated a study of the ...

Restriction and Ehresmann Semigroups

Inverse semigroups form a variety of unary semigroups, that is, semigroups equipped with an additional unary operation, in this case a 7→ a−1. The theory of inverse semigroups is perhaps the best developed within semigroup theory, and relies on two factors: an inverse semigroup S is regular, and has semilattice of idempotents. Three major approaches to the structure of inverse semigroups have e...

Finite semigroups as categories, ordered semigroups or compact semigroups

The results presented in this section are a good illustration of the following quotation of Marshall Stone [34]: ’A cardinal principle of modern mathematical research may be stated as a maxim: “One must always topologize” ’. Varieties of finite semigroups are a good example where Stone’s principle was applied successfully. Recall that a variety of semigroups is a class of semigroups closed unde...

Regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets

Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is anarbitrary mapping   from $S$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. In this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $S$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two m...