C-system of a module over a $Jf$-relative monad
Abstract
Let be the category with the set of objects and morphisms being the functions between the standard finite sets of the corresponding cardinalities. Let be the obvious functor from this category to the category of sets. In this paper we construct, for any relative monad on and a left module over , a C-system and explicitly compute the action of the B-system operations on its B-sets. In the following paper it is used to provide a rigorous mathematical approach to the construction of the C-systems underlying the term models of a wide class of dependent type theories. This paper is a result of evolution of arXiv:1407.3394. However this paper is much more detailed and contains a lot of material that is not contained in arXiv:1407.3394. It also does not cover some material that is covered in arXiv:1407.3394.
Cite
@article{arxiv.1602.00352,
title = {C-system of a module over a $Jf$-relative monad},
author = {Vladimir Voevodsky},
journal= {arXiv preprint arXiv:1602.00352},
year = {2016}
}