Subcategories and Products of Categories
نویسنده
چکیده
The subcategory of a category and product of categories is defined. The inclusion functor is the injection (inclusion) map E ↪→ which sends each object and each arrow of a Subcategory E of a category C to itself (in C). The inclusion functor is faithful. Full subcategories of C, that is, those subcategories E of C such that HomE(a,b) = HomC(b,b) for any objects a,b of E, are defined. A subcategory E of C is full when the inclusion functor E ↪→ is full. The proposition that a full subcategory is determined by giving the set of objects of a category is proved. The product of two categories B and C is constructed in the usual way. Moreover, some simple facts on bi f unctors (functors from a product category) are proved. The final notions in this article are that of projection functors and product of two functors (complex functors and product functors).
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