Concrete Categories
نویسنده
چکیده
In the paper, we develop the notation of duality and equivalence of categories and concrete categories based on [22]. The development was motivated by the duality theory for continuous lattices (see [10, p. 189]), where we need to cope with concrete categories of lattices and maps preserving their properties. For example, the category UPS of complete lattices and directed suprema preserving maps; or the category INF of complete lattices and infima preserving maps. As the main result of this paper it is shown that every category is isomorphic to its concretization (the concrete category with the same objects). Some useful schemes to construct categories and functors are also presented.
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