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For a pomonoid S, let us denote Pos-S the category of S-posets and S-poset maps. In this paper, we consider the slice cate- gory Pos-S/B for an S-poset B, and study some categorical ingredients. We first show that there is no non-trivial injective object in Pos-S/B. Then we investigate injective objects with respect to the class of regu- lar monomorphisms in this category and show that Pos-S/B has enough regular injective objects. We also prove that regular injective objects are retracts of exponentiable objects in this category. One of the main aims of the paper is to draw attention to characterizing injectivity in the cate- gory Pos-S/B under a particular case where B has trivial action. Among other things, we also prove that the necessary condition for a map (an ob- ject) here to be regular injective is being convex and present an example to show that the converse is not true, in general.
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참고문헌 (16)
참고문헌 신청
A. Bailey / 2014 / Weak factorization system for S-acts / Semigroup Forum 89 (1) : 52 ~ 67
A. Madanshekaf / 2001 / Tiny objects in the category of M-Sets / Ital. J. Pure Appl. Math 10 : 153 ~ 162
B. Banaschewski / 1967 / Categorical characterization of the MacNeille comple-tion / Arch. Math 18 : 369 ~ 377
B. Banaschewski / 1970 / Injectivity and essential extensions in equational classes of algebras / Proc. Conf. on Universal Algebra : 131 ~ 147
C. McLarty / 1992 / Elementary Categories, Elementary Toposes / Oxford University Press
A. Madanshekaf / 2001 / Tiny objects in the category of M-Sets / Ital. J. Pure Appl. Math 10 : 153 ~ 162
B. Banaschewski / 1967 / Categorical characterization of the MacNeille comple-tion / Arch. Math 18 : 369 ~ 377
B. Banaschewski / 1970 / Injectivity and essential extensions in equational classes of algebras / Proc. Conf. on Universal Algebra : 131 ~ 147
C. McLarty / 1992 / Elementary Categories, Elementary Toposes / Oxford University Press
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