### Continuous directed-complete ordered semigroups and their categorical properties

LIU Ni, ZHANG Miao-miao

1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
• Received:2015-06-08 Online:2016-06-20 Published:2016-06-15

Abstract: Firstly, the concept of continuous directed-complete ordered semigroup is introduced. Secondly, some equivalent characterizations of continuous directed-complete ordered semigroup are obtained. Finally, it is proved that the category CDOSG with objects all continuous directed-complete ordered semigroups and morphisms all ordered semigroup homomorphisms preserving directed sups between them is finite complete. Moreover, its full subcategory CCDOSG with objects all commutative continuous directed-complete ordered semigroups is finite complete and closed for function space.

CLC Number:

• O153
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