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The theory of semi-functors

  • Raymond Hoofman (a1)


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.



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Berry, G. (1987) Stable Models of Typed λ-Calculi. In: Ausiello, G. and Böhm, C. (eds.), Automata, Languages and Programming, Fifth Colloquium. Springer-Verlag Lect. Notes in Comp. Sci. 62 7289.
Freyd, P. A. and Scedrov, A. (1989) Categories, Allegories, North-Holland, Amsterdam.
Girard, J.-Y. (1986) The System F of Variable Types, Fifteen Years Later. Theor. Comput. Sci. 45 159192.
Girard, J.-Y. (1987) Linear Logic. Theor. Comput. Sci. 50 1102.
Hayashi, S. (1985) Adjunction of Semifunctors: Categorical Structures in Non-Extensional Lambda-Calculus. Theor. Comput. Sci. 41 95104.
Hoofman, R. (1992a) Continuous Information Systems. Information and Computation (to appear).
Hoofman, R. (1992b) Non-Stable Models of Linear Logic. Logical Foundations of Computer Science, Proceedings. Springer-Verlag Lect. Notes in Comp. Sci. (to appear).
Hoofman, R. (1992c) Non-Stable Models of Linear Logic, Ph.D. thesis, Utrecht University, Utrecht.
Hoofman, R., AND Schellinx, H. (1991) Collapsing Graph Models by Preorders. In: Pitt, D. H., Curien, P.-L., Abramsky, S., Pitts, A. M., Poigné, A. and Rydeheard, D. E. (eds.), Category Theory and Computer Science, Proceedings. Springer-Verlag Lect. Notes in Comp. Sci. 530 5373.
Jacobs, B. (1991) Semantics of Second Order Lambda Calculus. Mathematical Structures in Computer Science 1 (3).
Karoubi, M. (1978) K-theory, An Introduction, Springer, Berlin/New-York.
Koymans, C. P. J. (1982) Models of the Lambda Calculus. Inform. and Control 52 306322.
Kelly, G. M. and Street, R. (1974) Review of the Elements of 2-Categories. In: Category Seminar.Springer-Verlag Lect. Notes in Mathematics 420 75103.
Lambek, J. and Scott, P. J. (1986) Introduction to Higher Order Categorical Logic, Studies in Advanced Mathematics 7, Cambridge University Press.
Mac Lane, S. (1971) Categories for the Working Mathematician, Springer-Verlag, New-York.
Martini, S. (1987) An Interval Model for Second Order Lambda Calculus. In: Pitt, D. H., Poigné, A. and Rydeheard, D. (eds.), Category Theory and Computer Science, Proceedings. Springer-Verlag Lect. Notes in Comp. Sci. 283 219237.
Matsumoto, M. (1989) On the Yoneda Lemma and Adjunctions, Master’s Thesis, Dept. of Inform. Sci., Faculty of Sci., University of Tokyo.
Obtułowicz, A. and Wiweger, A. (1982) Categorical, Functional and Algebraic Aspects of the Type-Free Lambda Calculus. Universal Algebra and Applications, Banach Center Publications 9 399422.
Wiweger, A. (1984) Pre-adjunction and,λ-algebraic theories. Colloq. Math. 48 (2) 153165.

The theory of semi-functors

  • Raymond Hoofman (a1)


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