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math.LO2026
Dialectica Categories over Heyting Algebras
Colin Bloomfield, Peter Jipsen, Valeria de Paiva
Categorification---the process of constructing a categorical model of a piece of mathematics---often identifies a common abstraction that connects formerly unrelated but known stru…
math.LO2022
Fibered Universal Algebra for First-Order Logics
Colin Bloomfield, Yoshihiro Maruyama
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework…