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Abstract: . A coalgebra is introduced here as a model of a certain signature consisting of a type X with various "destructor" function symbols, satisfying certain equations. These destructor function symbols are like methods and attributes in object-oriented programming: they provide access to the type (or state) X. We show that the category of such coalgebras and structure preserving functions is comonadic over sets. Therefore we introduce the notion of a `mongruence' (predicate) on a coalgebra. It... (Update)
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0.5: Bisimulation and Apartness in Coalgebraic Specification - Jacobs (1995) (Correct)
0.4: A Tutorial on (Co)Algebras and (Co)Induction - Jacobs, Rutten (1997) (Correct)
0.4: Objects and Classes, Coalgebraically - Jacobs (1995) (Correct)
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22: An Approach to Object Semantics based on Terminal Co-algebras (context) - Reichel - 1995
22: Universal coalgebra: a theory of systems - Rutten - 1999
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BibTeX entry: (Update)
B. Jacobs. Mongruences and cofree coalgebras. In V.S. Alagar and M. Nivat, editors, Algebraic Methodology and Software Technology, number 936 in Lect. Notes Comp. Sci., pages 245-260. Springer, Berlin, 1995. http://citeseer.ist.psu.edu/jacobs95mongruences.html More
@inproceedings{ jacobs95mongruences,
author = "Bart Jacobs",
title = "Mongruences and Cofree Coalgebras",
booktitle = "Algebraic Methodology and Software Technology",
pages = "245-260",
year = "1995",
url = "citeseer.ist.psu.edu/jacobs95mongruences.html" }
Citations (may not include all citations):562 Categories for the Working Mathematician (context) - Lane - 1971
159 Non-well-founded sets (context) - Aczel - 1988
121 An approach to object semantics based on terminal co-algebra.. (context) - Reichel - 1995
91 A final coalgebra theorem (context) - Aczel, Mendler - 1989
69 Triples and Theories (context) - Barr, Wells - 1985
40 Object-oriented programming versus abstract data types (context) - Cook - 1990
23 Algebraic Theories (context) - Manes - 1974
13 Final data types and their specification (context) - Kamin - 1983
12 Also available as Aarhus Univ (context) - Hermida, Logical et al. - 1993
8 Induction and coinduction via subset types and quotient type.. (context) - Hermida, Jacobs - 1994
3 An abstract view of objects and subtyping (context) - Hofmann, Pierce - 1995
3 Parameters and parametrization in specification using distri.. (context) - Jacobs - 1995
1 Recent trends in Data Type Specification Springer LNCS (context) - Hensel, Reichel et al. - 1995
1 Manuscript available from ftp (context) - Jacobs, apartness et al. - 1995
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://ftp.cwi.nl/ftp/bjacobs/): More
Objects And Classes, Co-Algebraically - Jacobs (1996) (Correct)
Quotients in Simple Type Theory - Jacobs (1994) (Correct)
An Algebraic View of Structural Induction - Hermida, Jacobs (1994) (Correct)
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