Universal Algebra and Coalgebra

Front Cover
World Scientific, 2009 - Mathematics - 278 pages
The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.
 

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Contents

Introduction
1
1 Algebras and Identities
7
2 Statebased Systems
35
3 Basic Concepts from Category Theory
69
4 FCoalgebras
89
5 FAlgebras
113
6 F1 F2Coalgebras
129
7 Terminal Coalgebras
145
9 Coalgebras of Type
167
10 Clones of Operations and Cooperations
187
11 Semigroups of Operations and Cooperations
213
12 Cohyperidentities and Msolid Classes of Coalgebras
251
Bibliography
265
Glossary
271
Index
273
Copyright

8 Cofree Fcoalgebras and Coequations
155

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