Database Reference
In-Depth Information
by the, equivalent to it, “computation” morphism in DB ? Why is the Kleisly cat-
egory of the monad (power-view endofunctor) T isomorphic to the DB category,
and in which way may this Kleisly category be internalized in DB ? Show the
categorial definition of the query equivalence.
References
1. P. Aczel, J. Adamek, S. Milius, J. Velebil, Infinite trees and completely iterative theories: a
coalgebraic view. Theor. Comput. Sci. 300 , 1-45 (2003)
2. J. Adamek, J. Rosicky, Locally Presentable and Accessible Categories . London Mathematical
Society Lecture Note Series, vol. 189 (Cambridge University Press, Cambridge, 1994)
3. M. Barr, C. Wells, Toposes, Triples and Theories . Grundelehren der math. Wissenschaften,
vol. 278 (Springer, Berlin, 1985)
4. P.M. Cohn, Universal Algebra (Harper and Row, London, 1965)
5. E. Dubuc, Kan extensions in enriched category theory, in Lecture Notes in Math. , vol. 145
(Springer, Berlin, 1970), pp. 275-291
6. E. Dubuc, R. Street, Dinatural transformations, in Lecture Notes in Math. , vol. 137 (Springer,
Berlin, 1970), pp. 126-138
7. P. Gabriel, F. Ulmer, Lokal prasentierbare kategorien . Lecture Notes in Mathematics, vol. 221
(Springer, Berlin, 1971)
8. A.Y. Halevy, Theory of answering queries using views. SIGMOD Rec. 29 (4), 40-47 (2000)
9. B. Jacobs, J. Rutten, A tutorial on (co)algebras and (co)induction. Bull. Eur. Assoc. Theor.
Comput. Sci. 62 , 222-259 (1997)
10. G.M. Kelly, Basic Concepts of Enriched Category Theory . London Mathematical Society Lec-
ture Note Series, vol. 64 (Cambridge University Press, Cambridge, 1982)
11. G.M. Kelly, A.J. Power, Adjunctions whose counits are coequalizers, and presentations of
finitary enriched monads. J. Pure Appl. Algebra 89 , 163-179 (1993)
12. Y. Kinoshita, A.J. Power, M. Takeyama, Sketches. J. Pure Appl. Algebra 143 , 275-291 (1999)
13. C. Lair, Sur le genre d'esquissibilite des categories modelables (accessibles) possedant les
produits de deux. Diagrammes 35 , 25-52 (1996)
14. S.M. Lane, Categories for the Working Mathematician (Springer, Berlin, 1971)
15. F.W. Lawvere, Functorial semantics of algebraic theories. Proc. Natl. Acad. Sci. 50 , 869-872
(1963)
16. Z. Majkic, Abstract database category based on relational-query observations, in International
Conference on Theoretical and Mathematical Foundations of Computer Science (TMFCS-08) ,
Orlando FL, USA, July 7-9 (2008)
17. Z. Majkic, Algebraic operators for matching and merging of relational databases, in Interna-
tional Conference in Artificial Intelligence and Pattern Recognition (AIPR-09) , Orlando FL,
USA, July 13-16 (2009)
18. Z. Majkic, Induction principle in relational database category, in Int. Conference on Theoreti-
cal and Mathematical Foundations of Computer Science (TMFCS-09) , Orlando FL, USA, July
13-16 (2009)
19. Z.
Majkic,
DB
category:
denotational
semantics
for
view-based
database
mappings.
arXiv:1103.0217v1 (2011), 24 February, pp. 1-40
20. M. Makkai, R. Pare, Accessible Categories: The Foundations of Categorical Model Theory .
Contemporary Mathematics, vol. 104 (Am. Math. Soc., Providence, 1989)
21. E. Moggi, Computational lambda-calculus and monads, in Proc. of the 4th IEEE Symp. on
Logic in Computer Science (LICS'89) (1989), pp. 14-23
22. E. Moggi, Notions of computation and monads. Inf. Comput. 93 (1), 55-92 (1991)
23. A.J. Power, Enriched Lawvere theories. Theory Appl. Categ. 6 , 83-93 (2000)
24. M. Smith, G. Plotkin, The category-theoretic solution of recursive domain equations. SIAM J.
Comput. (1982)
Search WWH ::




Custom Search