The notion of tripos (Hyland, Johnstone, and Pitts 1980; Pitts 1981) was motivated by the desire to explain in what sense Higg’s description of sheaf toposes as H-valued sets and Hyland’s realizability toposes are instances of the same construction. The construction itself can be seen as the universal solution to the problem of realizing the predicates of a first order hyperdoctrine as subobjec...