Adjoint relations of S-fuzzy posets with some categories

In this paper, recalling the category FPos-S of all S-fuzzy posets, and action and order preserving maps between them, some categorical properties of the category FPos-S is studied. In particular, we characterize products, coproducts, equalizers, coequalizers, pullbacks and pushouts in this category. Also, all forgetful functors between the category FPos-S and the categories FPos of fuzzy posets, Pos-S, Pos, Act-S and Set are considered, and the existence of left and right adjoints of all mentioned forgetful functors are studied.

Keywords:

fuzzy poset , S-fuzzy poset , free , cofree , adjoint relations