On the Generators in the Category of Actions of Pomonoids on Posets and its Slices

Farideh Farsad; Ali Madanshekaf

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arXiv · 1503.05071

On the Generators in the Category of Actions of Pomonoids on Posets and its Slices

Farideh Farsad·Ali Madanshekaf

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Abstract

Let $S$ be a pomonoid, in this paper, {\bf Pos}-$S$, the category of $S$-posets and $S$-poset maps, is considered. First, we characterize some pomonoids on which all projectives in this category are generator or free. Then, we study regular injectivity and weakly regularly $d$-injectivity which lead to some homological classification results for pomonoids. Among other things, we get some relationships between regular injectivity in the slice category {\bf Pos}-$S/B_S$ and generators or cyclic projectives in {\bf Pos}-$S$.

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BibTeX RIS

Farideh Farsad, Ali Madanshekaf. 2015-03-17. On the Generators in the Category of Actions of Pomonoids on Posets and its Slices. https://arxiv.org/abs/1503.05071

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