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Algebras and Coalgebras || Algebraic and Coalgebraic Methods in the Mathematics of Program Construction

✍ Scribed by Backhouse, Roland; Crole, Roy; Gibbons, Jeremy

Book ID
111671569
Publisher
Springer Berlin Heidelberg
Year
2002
Tongue
German
Weight
166 KB
Edition
2002
Category
Article
ISBN
3540436138

No coin nor oath required. For personal study only.

✦ Synopsis

Program Construction Is About Turning Specifications Of Computer Software Into Implementations. Recent Research Aimed At Improving The Process Of Program Construction Exploits Insights From Abstract Algebraic Tools Such As Lattice Theory, Fixpoint Calculus, Universal Algebra, Category Theory, And Allegory Theory. This Textbook-like Tutorial Presents, Besides An Introduction, Eight Coherently Written Chapters By Leading Authorities On Ordered Sets And Complete Lattices, Algebras And Coalgebras, Galois Connections And Fixed Point Calculus, Calculating Functional Programs, Algebra Of Program Termination, Exercises In Coalgebraic Specification, Algebraic Methods For Optimization Problems, And Temporal Algebra. Ordered Sets And Complete Lattices -- Algebras And Coalgebras -- Galois Connections And Fixed Point Calculus -- Calculating Functional Programs -- Algebra Of Program Termination -- Exercises In Coalgebraic Specification -- Algebraic Methods For Optimization Problems -- Temporal Algebra. Roland Backhouse, Roy Crole, Jeremy Gibbons, Eds. Includes Bibliographical References And Index.

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Forms of Coalgebras and Hopf Algebras
Forms of Coalgebras and Hopf Algebras
✍ Darren B. Parker πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 237 KB

We study forms of coalgebras and Hopf algebras i.e., coalgebras and Hopf . algebras which are isomorphic after a suitable extension of the base field . We classify all forms of grouplike coalgebras according to the structure of their simple subcoalgebras. For Hopf algebras, given a W \*-Galois field