J. Lambek. A xpoint theorem for complete categories. Math. Z., 103:151-161, 1968. Home/Search Document Not in Database Summary Related Articles Check |
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μ-Bicomplete Categories and Parity Games - Santocanale (Correct)
....we de ne an initial F algebra to be an initial object in this category. More explicitly, an F algebra (x; is initial if for each F algebra (c; there exists a unique arrow f : x c such that f = Ff . We remark that if an F algebra (x; is initial, then the arrow is invertible [21]. F coalgebras and their morphisms are de ned dually and form a category CF . We recall that a coalgebra : y Fy is nal if for each coalgebra : c F c there exists a unique arrow g : c y such that g = Fg. If F : C D C is such that for every object d of D there exists an ....
J. Lambek. A xpoint theorem for complete categories. Math. Z., 103:151{ 161, 1968.
Mathematics of Recursive Program Construction - Doornbos, Backhouse (2001) (1 citation) (Correct)
....; f] is sometimes used. The initial algebra is also a parameter that is not made explicit; this is less of a problem because initial F algebras are isomorphic and thus catamorphisms are de ned up to isomorphism . An important property of initial algebras, commonly referred to as Lambek s lemma [18], is that an initial algebra is both injective and surjective. Thus, for example, zero 5 succ is an isomorphism between Nat and 11 Nat . Lambek s lemma has the consequence that, if in is an initial F algebra, h in = f F:h h = f F:h in [ where in [ is the inverse of in . Thus, the ....
J. Lambek. A xpoint theorem for complete categories. Mathematische Zeitschrift, 103:151-161, 1968.
Generic Programming With Relations and Functors - Bird, de Moor, Hoogendijk (1999) (6 citations) (Correct)
....by : T FT . For any other F algebra R : A FA the unique homomorphism from to R will be denoted by ( R] so ( R] A T is characterised by (X = R FX ) X = R] Homomorphisms of the form ( R] are called catamorphisms [18] The initial algebra is, in fact, an isomorphism [16] so we can rewrite the above equivalence in the form (X = R FX ) X = R] The well known Knaster Tarski Fixpoint Theorem says that the unique solution (if it exists) of X = F (X ) is also the least solution of X F (X ) and the greatest solution of X F (X ) so we get the ....
J. Lambek. A xpoint theorem for complete categories. Mathematische Zeitschrift, 103:151-161, 1968.
Fixed Point Calculus - Backhouse (2000) (5 citations) (Correct)
....; f] is sometimes used. The initial algebra is also a parameter that is not made explicit; this is less of a problem because initial F algebras are isomorphic and thus catamorphisms are de ned up to isomorphism . An important property of initial algebras, commonly referred to as Lambek s lemma [Lam68] is that an initial algebra is both injective and surjective. Thus, for example, zero 5 succ is an isomorphism between IN and 11 IN . Lambek s lemma has the consequence that, if in is an initial F algebra, h2 f FAlg in h = f F:h in [ where in [ is the inverse of in . Thus, the ....
J. Lambek. A xpoint theorem for complete categories. Mathematische Zeitschrift, 103:151-161, 1968.
A Calculus of Circular Proofs and its Categorical Semantics - Santocanale (2002) (2 citations) (Correct)
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J. Lambek. A xpoint theorem for complete categories. Math. Z., 103:151-161, 1968.
On the Equational Definition of the Least Prefixed Point - Santocanale (2003) (Correct)
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J. Lambek. A xpoint theorem for complete categories. Math. Z., 103:151{ 161, 1968. 29
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