Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-19T02:21:34.490Z Has data issue: false hasContentIssue false
  • English
  • Français

A remark on the theory of semi-functors

Published online by Cambridge University Press:  04 March 2009

R. Hoofman  and
I. Moerdijk
R. Hoofman
Affiliation:
University of Amsterdam Email: raymond@fwi.uva.nl
I. Moerdijk
Affiliation:
University of Utrecht Email: moerdijk@math.ruu.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

By establishing an appropriate equivalence, we observe that the theory of semi-functors can be fully embedded in the theory of (ordinary) functors. As a result, standard properties and constructions on functors extend automatically to semi-functors.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 1 , March 1995 , pp. 1 - 8
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bénabou, J. (1985) Fibred Categories and the Foundations of Naive Category Theory. J. Symb. Log. 50 10–37.CrossRefGoogle Scholar
Freyd, P. A. and Scedrov, A. (1989) Categories, Allegories, North-Holland, Amsterdam.Google Scholar
Hayashi, S. (1985) Adjunction of Semifunctors: Categorical Structures in Non-Extensional Lambda- Calculus. Theor. Comput. Sci. 41 95–104.CrossRefGoogle Scholar
Hoofman, R. (1992) Non-Stable Models of Linear Logic. In: Nerode, A. and Taitslin, M. (eds.) Logical Foundations of Computer Science. Springer-Verlag Lecture Notes in Computer Science 620 209–220.CrossRefGoogle Scholar
Hoofman, R. (1993a) The Theory of Semi-Functors. Mathematical Structures in Computer Science 3 93–128.CrossRefGoogle Scholar
Hoofman, R. (1993b) Information Systems as Coalgebras, ILLC Prepublication Series, ML-92–08, University of Amsterdam.Google Scholar
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. Springer-Verlag Lecture Notes in Computer Science 530 53–73.CrossRefGoogle Scholar
Hoofman, R. and Moerdijk, I. (1994) On the Extensionalization of Second-Order Models (manuscript).Google Scholar
Jacobs, B. (1991) Semantics of the Second Order Lambda Calculus. Mathematical Structures in Computer Science 1 327–360.CrossRefGoogle Scholar
Koymans, C. P. J. (1982) Models of the Lambda Calculus. Information and Control 52 306–322.CrossRefGoogle Scholar
Kelly, G. M. and Street, R. (1974) Review of the Elements of 2-Categories, Category Seminar. Springer-Verlag Lecture Notes in Mathematics 420 75–103.CrossRefGoogle Scholar
Lambek, J. and Scott, P. J. (1986) Introduction to Higher Order Categorical Logic, Studies in Advanced Mathematics 7, Cambridge University Press.Google Scholar
Mac Lane, S. (1971) Categories for the Working Mathematician, Springer-Verlag, New York.CrossRefGoogle Scholar
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. Springer-Verlag Lecture Notes in Computer Science 283 219–237.CrossRefGoogle Scholar
Martini, S. (1992) Categorical Models for Non-Extensional λ-Calculi and Combinatory Logic. Mathematical Structures in Computer Science 2 327–357.CrossRefGoogle Scholar
Román, L. (1989) On Partial Cartesian Closed Categories. In: Gray, J. W. and Scedrov, A. (eds.) Categories in Computer Science and Logic. Contemporary Mathematics 92, American Mathematical Society 349–356.CrossRefGoogle Scholar
Seely, R. A. G. (1987) Categorical Semantics for Higher Order Polymorphic Lambda Calculus. J. Symb. Logic. 52 145–156.CrossRefGoogle Scholar
Street, R. (1972) The Formal Theory of Monads. Journal of Pure and Applied Algebra 2 149–168.CrossRefGoogle Scholar