A 2-Categorical Analysis of the Tripos-to-Topos Construction

Details A 2-Categorical Analysis of the Tripos-to-Topos Construction A 2-Categorical Analysis of the Tripos-to-Topos Construction

2011-04-14

arxiv.org/abs/1104.2776v1

Mathematics

Category Theory

Scientific paper

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.

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