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Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties:...
The aim of this paper is to construct an -valued category whose objects are --ordered sets. To reach the goal, first, we construct a category whose objects are --ordered sets and morphisms are order-preserving mappings (in a fuzzy sense). For the morphisms of the category we define the degree to which each morphism is an order-preserving mapping and as a result we obtain an -valued category. Further we investigate the properties of this category, namely, we observe some special objects, special...
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