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Jaap van Oosten works on category theory, the theory of the topos and realizability, connecting mathematical structures with models of computation. Utrecht's publication record verifies this research program.^[ref]

His Topos Theory by Jaap van Oosten (2018) explains how categorical structure can transport logical constructions. Its adjoint lifting theorem for monad algebra functors builds an adjoint at an algebraic level from an adjunction and suitable presentations underneath. The notes apply this to logical functors using power-object structure, making precise when a familiar construction survives passage to a richer category.^[ref]

Authored lecture notes by Jaap van Oosten, Utrecht University. Theorem0.11, printed pp.x–xii, states the adjoint lifting theorem and constructs the lifted adjoint from reflexive presentations. Theorem1.16 applies lifting to logical functors through power-object monadicity.