Loading [MathJax]/extensions/MathZoom.js
In the first part of this article we formalize the concepts of terminal and initial object, categorical product [4] and natural transformation within a free-object category [1]. In particular, we show that this definition of natural transformation is equivalent to the standard definition [13]. Then we introduce the exponential object using its universal property and we show the isomorphism between the exponential object of categories and the functor category [12].
Let be a partially ordered abelian group (-group). The construction of the Lorenzen ideal -system in is investigated and the functorial properties of this construction with respect to the semigroup of all -ideal systems defined on are derived, where for and a lower bounded subset , . It is proved that Lorenzen construction is the natural transformation between two functors from the category of -groups with special morphisms into the category of abelian ordered semigroups.
Currently displaying 1 –
9 of
9