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An introduction to fibrations, topos theory, the effective topos and modest sets Transplant with a number of theThis book describes Hyland's effective topos, which provides a category theoretic realizability model of higher order type theory and quantification over types. Along the way, it provides an introduction to fibrations and topos theory, suitable for readers with a basic background in mathematical logic and category theory. It is based on a 1992 lecture series at the University of Edinburgh.