A C-SYSTEM DEFINED BY A UNIVERSE CATEGORY

作者：Voevodsky Vladimir^*

来源：Theory and Applications of Categories, 2015, 30: 1181-1214.

• contextual category
• universe category
• C-system

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 : (U) over tilde -> 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.

• 出版日期2015