Restriction categories II: Partial map classification

Theoretical Computer Science

Volumn 294, Issue 1-2, 2003, Pages 61-102

  Cockett, J R B ^a   Lack, Stephen ^b  

^a UNIVERSITY OF CALGARY   (Canada)

^b UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Kleisli category; Monad; Partial map classifier; Restriction category

Indexed keywords

ALGEBRA; CLASSIFICATION (OF INFORMATION); INFORMATION SCIENCE; SEMANTICS;

PARTIAL MAP CLASSIFICATION;

COMPUTER SCIENCE;

EID: 0037441259     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(01)00245-6     Document Type: Conference Paper

References (20)

1. J. Bénabou, Introduction to bicategories, Reports of the Midwest Category Seminar, Lecture Notes in Mathematics, Vol. 106, 1967, pp. 1-77.
2. A. Bucalo, C. Führmann, A. Simpson, An equational notion of lifting monads, Theoret. Comput. Sci. this Vol. (2003).
3. Carboni A. Bicategories of partial maps. Cah. de Top. Geom. Differential. 28:1987;111-126.
4. J.R.B. Cockett, S. Lack, Restriction categories I: categories of partial maps, Theoret. Comput. Sci. 270 (2001) 223-259. Available electronically from http://www.maths.usyd.edu.au/u/stevel/papers/resti.html.
5. J.R.B. Cockett, S. Lack, Restriction categories III: partial structures, in preparation.
6. J.R.B. Cockett, D. Spencer, Strong categorical datatypes I, Category Theory 1991 (Montreal, PQ, 1991) CMS Conf. Proc. 13, Amer. Math. Soc., Providence RI, 1992, pp. 141-169.
7. Di Paola R.A., Heller A. Dominical categories: recursion theory without elements. J. Symbolic Logic. 52:1987;595-635.
8. Führmann C. Direct Models of the Computational Lambda-Calculus, MFPS XV (= Electron. Notes Theor. Comput. Sci., Vol. 20. 1999;Elsevier, Amsterdam.
9. Johnstone P.T. Topos Theory, L.M.S Monographs. Vol. 10:1977;Academic Press, London.
10. Johnstone P.T. Variations on the bagdomain theme. Theoret. Comput. Sci. 136:1994;3-20.
11. Kelly G.M., Power A.J. Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads. J. Pure Appl. Algebra. 89:1993;163-179.
12. Kock A. Strong functors and monoidal monads. Arch. Math. 23:1972;113-120.
13. Manes E.G. Algebraic Theories. 1976;Springer, New York.
14. Mulry P.S. Partial map classifiers and partial cartesian closed categories. Theoret. Comput. Sci. 99:1992;141-155.
15. Mulry P.S. Monads and algebras in the semantics of partial data types. Theoret. Comput. Sci. 136:1994;109-123.
16. Mulry P.S. Lifting theorems for Kleisli categories, Mathematical Foundations of Programming Semantics, Lecture Notes in Computer Science. Vol. 802:1994;Springer, Berlin.
17. Robinson E.P., Rosolini G. Categories of partial maps. Inform. and Comput. 79:1988;94-130.
18. G. Rosolini, Continuity and effectiveness in topoi, D.Phil Thesis, Oxford University, 1986.
19. Street R.H. The formal theory of monads. J. Pure Appl. Algebra. 2:1972;149-168.
20. J.R.B. Cockett, S. Lack, The extensive completion of a distributive category, Theory Appl. Categ. 8 (2001) 541-554. Available electronically from http://www.maths.usyd.ad/u/stevel/papers/extcomp.html.