The Category of S-Posets |
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Authors: | Sydney Bulman-Fleming Mojgan Mahmoudi |
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Institution: | (1) Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada;(2) Department of Mathematics, Shahid Beheshti University, Tehran 19839, Iran |
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Abstract: | In this paper, we consider some category-theoretic properties of the
category Pos-S of all S-posets (posets equipped with a compatible right action of a pomonoid S), with monotone action-preserving
maps between them. We first discuss some general category-theoretic ingredients of Pos-S; specifically, we characterize several
kinds of epimorphisms and monomorphisms. Then, we present some adjoint relations of Pos-S with Pos, Set, and Act-S. In particular,
we discuss free and cofree objects. We also examine other category-theoretic properties, such as cartesian closedness and
monadicity. Finally, we consider projectivity in Pos-S with respect to regular epimorphisms and show that it is the same asprojectivity,
although projectives are not generally retracts of free
objects over posets. |
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Keywords: | |
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