JP Journal of Algebra, Number Theory and Applications
Volume 9, Issue 1, Pages 1 - 36
(October 2007)
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ON A CLASS OF PARTIAL FUNCTORS BETWEEN CATEGORIES WHICH PROVIDE A CLOSED AND ORDERED PARTIALLY ADDITIVE CATEGORY OF CATEGORIES
J. Climent Vidal (Spain) and J. Soliveres Tur (Spain)
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Abstract: We single out a class of partial functors, the partial supersaturated functors, together with the associated partial natural transformations between them, which allows us to get a symmetric monoidal closed, non-cartesian, and ordered partially additive category with small categories as objects and morphisms the partial supersaturated functors. Moreover, we extend some notions and constructions from semigroup theory, e.g., Rees congruences, Rees homomorphisms and ideal extensions, to categories and partial supersaturated functors. Also, we state a Yoneda-Grothendieck Lemma for the above class of partial functors and generalize the concept of adjunction to that of partial adjunction, providing for this last concept one fundamental example from the field of algebraic logic. |
Keywords and phrases: partial supersaturated functor, supersaturated subcategory, partial natural transformation, Rees functor, Rees congruence, extension of a category by another, subidentity, partial adjunction. |
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