A C-system Defined by a Universe Category
نویسنده
چکیده
This is the third paper in a series started in [9]. In it we construct a C-system CC(C, p) starting from a category C together with a morphism p : Ũ → U , a choice of pull-back squares based on p for all morphisms to U and a choice of a final object of C. Such a quadruple is called a universe category. We then define universe category functors and construct homomorphisms of C-systems CC(C, p) defined by universe category functors. In the sections before the last section we give, for any C-system CC, three different constructions of pairs ((C, p), H) where (C, p) is a universe category and H : CC → CC(C, p) is an isomorphism. In the last section we construct for any (set) category C with a choice of a final object and fiber products a C-system and an equivalence between C and the precategory underlying CC.
منابع مشابه
C-systems Defined by Universe Categories: Presheaves
The main result of this paper may be stated as a construction of “almost representations” μn and μ̃n for the presheaves Obn and Õbn on the C-systems defined by locally cartesian closed universe categories with binary product structures and the study of the behavior of these “almost representations” with respect to the universe category functors. In addition, we study a number of constructions on...
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