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The theory of semi-functors

Published online by Cambridge University Press:  04 March 2009

Raymond Hoofman
Raymond Hoofman
Affiliation:
Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
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Abstract

The notion of semi-functor was introduced in Hayashi (1985) in order to make possible a category-theoretical characterization of models of the non-extensional typed lambda calculus. Motivated by the further use of semi-functors in Martini (1987), Jacobs (1991) and Hoofman (1992a), (1992b) and (1992c), we consider the general theory of semi-functors in this paper. It turns out that the notion of semi natural transformation plays an important part in this theory, and that various categorical notions involving semi-functors can be viewed as 2-categorical notions in the 2-category of categories, semi-functors and semi natural transformations. In particular, we find that the notion of normal semi-adjunction as defined in Hayashi (1985) is the canonical generalization of the notion of adjunction to the world of semi-functors. Further topics covered in this paper are the relation between semi-functors and splittings, the Karoubi envelope construction, semi-comonads, and a semi-adjoint functor theorem.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 3 , Issue 1 , March 1993 , pp. 93 - 128
Copyright
Copyright © Cambridge University Press 1993

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