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  • Every finitary endofunctor H of Set can be represented via a finitary signature Sigma and a collection of equations called %22basic%22. We describe a terminal coalgebra for Has the terminal Sigma-coalgebra (of all E-trees) modulo the congruence of applying the basic equations potentially infinitely often. As an application we describe a free iterative theory on H (in the sense of Calvin Elgot) as the theory of all rational E-trees modulo the analogous congruence. This yields a number of new examples of iterative theories, e.g., the theory of all strongly extensional, rational, finitely branching trees, free on the finite power-set functor, or the theory of all binary, rational unordered trees, free on one commutative binary operation. (c) 2006 Elsevier Inc. All rights reserved.
  • Every finitary endofunctor H of Set can be represented via a finitary signature Sigma and a collection of equations called %22basic%22. We describe a terminal coalgebra for Has the terminal Sigma-coalgebra (of all E-trees) modulo the congruence of applying the basic equations potentially infinitely often. As an application we describe a free iterative theory on H (in the sense of Calvin Elgot) as the theory of all rational E-trees modulo the analogous congruence. This yields a number of new examples of iterative theories, e.g., the theory of all strongly extensional, rational, finitely branching trees, free on the finite power-set functor, or the theory of all binary, rational unordered trees, free on one commutative binary operation. (c) 2006 Elsevier Inc. All rights reserved. (en)
Title
  • Terminal Coalgebras and Free Iterative Theories
  • Terminal Coalgebras and Free Iterative Theories (en)
skos:prefLabel
  • Terminal Coalgebras and Free Iterative Theories
  • Terminal Coalgebras and Free Iterative Theories (en)
skos:notation
  • RIV/68407700:21230/06:00124026!RIV10-MSM-21230___
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  • RIV/68407700:21230/06:00124026
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  • algebra; Free Iterative Theories (en)
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  • US - Spojené státy americké
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  • [39B254E1CFAB]
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  • Information and Computation
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  • 204
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  • Adámek, Jiří
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  • 000238782700005
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  • 0890-5401
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  • 21230
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