A 2-Categorical Analysis of the Tripos-to-Topos Construction
Category Theory
2011-04-15 v1
Abstract
We characterize the tripos-to-topos construction of Hyland, Johnstone and Pitts as a biadjunction in a bicategory enriched category of equipment-like structures. These abstract concepts are necessary to handle the presence of oplax constructs --- the construction is only oplax functorial on certain classes of cartesian functors between triposes. A by-product of our analysis is the decomposition of the tripos-to-topos construction into two steps, the intermediate step being a weakened version of quasitoposes.
Cite
@article{arxiv.1104.2776,
title = {A 2-Categorical Analysis of the Tripos-to-Topos Construction},
author = {Jonas Frey},
journal= {arXiv preprint arXiv:1104.2776},
year = {2011}
}