Abstract
We describe a part of the theory of classifying topoi and its connections with various topics from computer science, logic, and algebra.
For Yuri Gurevich on the occasion of his eightieth birthday
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Notes
- 1.
We adopt the “logical” convention that a morphism in this category is a natural transformation between the left-adjoint parts \(f^*\) of two geometric morphisms. The “geometric” convention would use the right-adjoint parts instead and would result in a category dual to ours.
- 2.
The additional modifications involved a group action and a probability distribution on the set of “truth values” of the predicates, a set that was not required to contain only “true” and “false”. In our present, functional situation, there are no truth values, and so those modifications are not applicable.
References
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Blass, A. (2020). Functional Thesauri, Classifying Topoi, Unification, and Flatness. In: Blass, A., Cégielski, P., Dershowitz, N., Droste, M., Finkbeiner, B. (eds) Fields of Logic and Computation III. Lecture Notes in Computer Science(), vol 12180. Springer, Cham. https://doi.org/10.1007/978-3-030-48006-6_4
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