# Free and Cofree Acts of Dcpo-Monoids on Directed Complete Posets

Bulletin of the Malaysian Mathematical Sciences Society, May 2015

In this paper, we study the existence of the free and cofree objects in the categories Dcpo-$$S$$ (and Cpo-$$S$$) of all directed complete posets (with bottom element) equipped with a compatible right action of a dcpo-monoid (cpo-monoid) $$S$$, with (strict) continuous action-preserving maps between them. More precisely, we consider all forgetful functors between these categories and the categories Dcpo of dcpo’s, (CPo) of cpo’s, Pos of posets, and Set of sets, and study the existence of their left and right adjoints.

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Mojgan Mahmoudi, Halimeh Moghbeli. Free and Cofree Acts of Dcpo-Monoids on Directed Complete Posets, Bulletin of the Malaysian Mathematical Sciences Society, 2015, 589-603, DOI: 10.1007/s40840-015-0127-z