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Abstract: : This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for each concept, but completeness is not attempted. Some additional categorical concepts and some suggestions for further research are also mentioned. The paper concludes with some philosophical... (Update)
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BibTeX entry: (Update)
J.A. Goguen. A categorical manifesto. Math. Struct. Comp. Sci., 1(1):49--67, 1991. http://citeseer.ist.psu.edu/goguen91categorical.html More
@article{ goguen91categorical,
author = "Joseph A. Goguen",
title = "A Categorical Manifesto",
journal = "Mathematical Structures in Computer Science",
volume = "1",
number = "1",
pages = "49-67",
year = "1991",
url = "citeseer.ist.psu.edu/goguen91categorical.html" }
Citations (may not include all citations):562 Categories for the Working Mathematician (context) - Lane - 1971
359 Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
243 An Introduction to Unification-Based Approaches to Grammar (context) - Shieber - 1986
215 Theoretical Computer Science (context) - Raoult, rewritings - 1984
204 Lecture Notes in Computer Science (context) - Milner, of et al. - 1980
173 An initial algebra approach to the specification (context) - Goguen, Thatcher et al. - 1978
116 Introduction to the algebraic theory of graph grammars (context) - Ehrig - 1979
113 Functorial semantics of algebraic theories (context) - Lawvere - 1963
109 Putting theories together to make specifications (context) - Burstall, Goguen - 1977
109 Continuous lattices (context) - Scott - 1972
106 An algebraic definition of simulation between programs (context) - Milner - 1971
69 induction and computability (context) - Meseguer, Goguen - 1985
57 Some fundamental algebraic tools for the semantics of comput.. - Goguen, Burstall - 1984
57 Some fundamental algebraic tools for the semantics of comput.. - Goguen, Burstall - 1984
51 Recherches sur la th'eorie de la d'emonstration (context) - Herbrand - 1930
48 Laboratory for Foundations of Computer Science (context) - Moggi, monads et al. - 1988
48 Laboratory for Foundations of Computer Science (context) - Moggi, account et al. - 1989
45 Jean-Pierre Jouannaud (context) - Futatsugi, Goguen - 1985
41 Models and equality for logical programming (context) - Goguen, Meseguer - 1987
39 The effective topos (context) - Hyland - 1982
38 Allyn and Bacon (context) - Herrlich, Strecker - 1973
29 A categorical approach to general systems theory (context) - Goguen, Ginali - 1978
28 a system for the structured elaboration of correct programs .. (context) - Goguen, Burstall - 1980
19 the Categorial Analysis of Logic (context) - Goldblatt - 1979
19 Mathematical representation of hierarchically organized syst.. (context) - Goguen - 1971
18 On graph rewritings (context) - Kennaway - 1987
18 Grundlehren der mathematischen Wissenschafter (context) - Barr, Wells et al. - 1985
14 Formal Specification of Parameterized Programs in lilleanna (context) - Tracz
14 Petri nets are monoids: A new algebraic foundation for net t.. (context) - Meseguer, Montanari - 1988
11 Minimal realization of machines in closed categories (context) - Goguen - 1972
10 DACTL: Some introductory papers (context) - Glauert, Hammond et al. - 1988
10 Jungle evaluation for efficient term rewriting (context) - Hoffmann, Plump - 1988
10 Software for the Rewrite Rule Machine (context) - Goguen, Meseguer - 1988
9 The Logical Foundations of Mathematics (context) - Hatcher - 1982
8 Parameterized programming in OBJ (context) - Futatsugi, Goguen et al. - 1987
8 Process and Reality (context) - Whitehead - 1969
8 Mathematical System Theory (context) - Goguen, universal - 1973
8 A junction between computer science and category theory (context) - Goguen, Thatcher et al. - 1973
6 Programming Research Group (context) - Hoare, He et al. - 1988
5 CSLI Lecture Notes (context) - Aczel, Center et al. - 1988
5 The formal description of data types using sketches (context) - Barr, Wells - 1988
5 Duality for groups (context) - Lane - 1948
5 Lecture Notes in Mathematics (context) - Par'e, Johnstone et al. - 1978
4 An algebraic description of programs with assertions (context) - Burstall - 1972
3 Transactions of the American Mathematical Society (context) - Eilenberg, Lane et al. - 1945
3 ene Kirchner, Aristide M (context) - Goguen, Kirchner - 1988
3 New Science Library (context) - Maturana, Varela et al. - 1987
3 Research Notes in Theoretical Computer Science (context) - Curien, Sequential et al. - 1986
2 Unifying Models of Concurrency (context) - Ferrari - 1990
1 implementation and parameterization of abstract data types (context) - Ehrich, theory - 1982
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