Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Products of families of types in the C-systems defined by a universe
  category   We introduce the notion of a $(\Pi,\lambda)$-structure on a C-system and show
that C-systems with $(\Pi,\lambda)$-structures are constructively equivalent to
contextual categories with products of families of types. We then show how to
construct $(\Pi,\lambda)$-structures on C-systems of the form $CC({\cal C},p)$
defined by a universe $p$ in a locally cartesian closed category $\cal C$ from
a simple pull-back square based on $p$. In the last section we prove a theorem
that asserts that our construction is functorial.
  This version introduces some changes compared to the previous one to ensure
rigorous compatibility with arXiv:1409.7925v3.

30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat