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  • Dana Scott's model of lambda-calculus was based on a limit construction which started from an algebra of a suitable endofunctor F and continued by iterating F. We demonstrate that this is a special case of the concept we call coalgebra relatively terminal w.r.t. the given algebra A. This means a coalgebra together with a universal coalgebra-to-algebra morphism into A. We prove that by iterating F countably many times we obtain the relatively terminal coalgebras whenever F preserves limits of omega(op)-chains. If F is unitary, we need in general omega + omega steps. And for arbitrary accessible (=bounded) set functors we need an ordinal number of steps in general. Scott's result is captured by the fact that in a CPO-enriched category, assuming that F is locally continuous, omega steps are sufficient for algebras given by projections.
  • Dana Scott's model of lambda-calculus was based on a limit construction which started from an algebra of a suitable endofunctor F and continued by iterating F. We demonstrate that this is a special case of the concept we call coalgebra relatively terminal w.r.t. the given algebra A. This means a coalgebra together with a universal coalgebra-to-algebra morphism into A. We prove that by iterating F countably many times we obtain the relatively terminal coalgebras whenever F preserves limits of omega(op)-chains. If F is unitary, we need in general omega + omega steps. And for arbitrary accessible (=bounded) set functors we need an ordinal number of steps in general. Scott's result is captured by the fact that in a CPO-enriched category, assuming that F is locally continuous, omega steps are sufficient for algebras given by projections. (en)
Title
  • Relatively terminal coalgebras
  • Relatively terminal coalgebras (en)
skos:prefLabel
  • Relatively terminal coalgebras
  • Relatively terminal coalgebras (en)
skos:notation
  • RIV/00216208:11320/12:10133214!RIV13-MSM-11320___
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  • 164877
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  • RIV/00216208:11320/12:10133214
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  • terminal; coalgebra (en)
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  • NL - Nizozemsko
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  • [09C5720B4864]
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  • Journal of Pure and Applied Algebra
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  • 216
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  • Trnková, Věra
  • Adamek, Jiří
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  • 000305670800017
issn
  • 0022-4049
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  • 10.1016/j.jpaa.2012.02.026
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  • 11320
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