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Logical Construction of Final Coalgebras
, 2003
"... We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object. ..."
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We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object.
Abstract CMCS’03 Preliminary Version Logical Construction of Final Coalgebras
"... We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and ..."
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We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and
CMCS'03 Preliminary Version Logical Construction of Final Coalgebras
"... Abstract We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object. 1 Introduction In this note we prove that every polynomial endofunct ..."
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Abstract We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object. 1 Introduction In this note we prove that every polynomial endofunctor
ENRICHED INDEXED CATEGORIES
"... Abstract. We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an Sindexed monoidal category V. This includes classical enriched categories, indexed and fibered categories, and internal categories as special cases. ..."
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Abstract. We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an Sindexed monoidal category V. This includes classical enriched categories, indexed and fibered categories, and internal categories as special cases. We then describe the appropriate notion of “limit ” for such enriched indexed categories, and show that they admit “free cocompletions” constructed as usual with a Yoneda embedding.