Geodesic
C-systems defined by universe categories: presheaves
Theory and applications of categories, Tome 32 (2017), pp. 53-112.

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The main result of this paper may be stated as a construction of "almost representations" $\mu_n$ and $\tilde{\mu}_n$ for the presheaves $\Ob_n$ and $\tilde{Ob}_n$ 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 presheaves on C-systems and on universe categories that are used in the proofs of our main results, but are expected to have other applications as well.
Publié le :
Classification : 03F50, 18C50, 18D15
Keywords: Type theory, Contextual category, Universe category 
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     author = {Vladimir Voevodsky},
     title = {C-systems defined by universe categories: presheaves},
     journal = {Theory and applications of categories},
     pages = {53--112},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a2/}
}
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Vladimir Voevodsky. C-systems defined by universe categories: presheaves. Theory and applications of categories, Tome 32 (2017), pp. 53-112. http://geodesic.mathdoc.fr/item/TAC_2017_32_a2/