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Topic: Coalgebra

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	Abstract of: Universal coalgebra: a theory of systems
		Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems.
		Such a principle was missing for coalgebras until the work of Aczel (1988) on a theory of non-wellfounded sets, in which he introduced a proof principle nowadays called coinduction.
		Some standard results from universal algebra are reformulated (using the afore mentioned correspondence) and proved for a large class of coalgebras, leading to a series of results on, e.g., the lattices of subcoalgebras and bisimulations, simple coalgebras and coinduction, and a covariety theorem for coalgebras similar to Birkhoff's variety theorem.
	db.cwi.nl /rapporten/abstract.php?abstractnr=604 (276 words)

	PlanetMath: comodule coalgebra
		See Also: module algebra, module coalgebra, comodule algebra
		Cross-references: coaction, adjoint, Hopf algebra, algebra, coalgebra, right, bialgebra
		This is version 4 of comodule coalgebra, born on 2003-02-09, modified 2003-11-18.
	planetmath.org /encyclopedia/ComoduleCoalgebra.html (61 words)

	PlanetMath: coalgebra
		A coalgebra is said to be cocommutative if
		This is version 9 of coalgebra, born on 2002-10-18, modified 2005-02-02.
		Object id is 3522, canonical name is Coalgebra.
	planetmath.org /encyclopedia/Coassociative.html (76 words)

	Coalgebra Workshop
		Coalgebra is beginning to develop into a field of its own, with its own proof-methods (involving bisimulations and invariants).
		This workshop will be devoted to both an introduction to basic coalgebraic notions and techniques, and also to some recent advances in the theory of coalgebras.
		In particular, a tutorial is available, containing an introduction to coalgebras and coinduction (with many references).
	www.cs.ru.nl /~bart/coalg_worksh.html (510 words)

	Kestrel Institute - Research Staff - Dusko Pavlovic - Coalgebra
		The applications of the presented categorical analysis span across the gamut of the applications of coinduction, from modelling of computation to solving differential equations.
		This makes an attractive analogy with the definition of the ordinal omega itself as the initial algebra of the functor prepending the unity, with both definitions made in the category of posets.
		The elements of the final coalgebra are thus natural representatives of bisimilarity classes, and a denotational semantics of processes can be developed in a final-coalgebra-enriched category where arrows are processes, canonically represented.
	www.kestrel.edu /home/people/pavlovic/coalgebra.html (513 words)

	CiteULike: A Concrete Final Coalgebra Theorem for ZF Set Theory (Site not responding. Last check: 2007-10-13)
		A special final coalgebra theorem, in the style of Aczel's [2], is proved within standard Zermelo-Fraenkel set theory.
		Analogues of Aczel's Solution and Substitution Lemmas are proved in the style of Rutten and Turi [12].
		category-theory category-thoery coalgebra domain-theory functional haskell ilp linear-logic logic no-tag polymorphism topology type-theory
	www.citeulike.org /user/msakai/article/615982 (254 words)

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