C-systems defined by universe categories: presheaves
Abstract
The main result of this paper may be stated as a construction of "almost representations" for the canonical presheaves of object extensions of length 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.
Cite
@article{arxiv.1706.03620,
title = {C-systems defined by universe categories: presheaves},
author = {Vladimir Voevodsky},
journal= {arXiv preprint arXiv:1706.03620},
year = {2017}
}
Comments
The paper introduces and studies "canonical" presheaves on C-systems defined by universe categories. It is the second of the three papers into which the preprint "Products of families of types in the C-systems defined by a universe category" evolved during publication. The paper is published in Theory and Applications of Categories