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- Initial_algebra abstract "In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. The initiality provides a general framework for induction and recursion. For instance, consider the endofunctor 1+(-) on the category of sets, where 1 is the one-point set, the terminal object in the category. An algebra for this endofunctor is a set X (called the carrier of the algebra) together with a point x ∈ X and a function X→X. The set of natural numbers is the carrier of the initial such algebra: the point is zero and the function is the successor map. For a second example, consider the endofunctor 1+N×(-) on the category of sets, where N is the set of natural numbers. An algebra for this endofunctor is a set X together with a point x ∈ X and a function N×X → X. The set of finite lists of natural numbers is the initial such algebra. The point is the empty list, and the function is cons, taking a number and a finite list, and returning a new finite list with the number at the head.".
- Initial_algebra wikiPageExternalLink rutten94initial.html.
- Initial_algebra wikiPageExternalLink free-rectypes.txt.
- Initial_algebra wikiPageExternalLink initiality_20and_20finality.html.
- Initial_algebra wikiPageExternalLink thesis.pdf.
- Initial_algebra wikiPageID "4116488".
- Initial_algebra wikiPageRevisionID "549097379".
- Initial_algebra hasPhotoCollection Initial_algebra.
- Initial_algebra subject Category:Category_theory.
- Initial_algebra subject Category:Functional_programming.
- Initial_algebra subject Category:Type_theory.
- Initial_algebra comment "In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. The initiality provides a general framework for induction and recursion. For instance, consider the endofunctor 1+(-) on the category of sets, where 1 is the one-point set, the terminal object in the category. An algebra for this endofunctor is a set X (called the carrier of the algebra) together with a point x ∈ X and a function X→X.".
- Initial_algebra label "Initial algebra".
- Initial_algebra label "始代数".
- Initial_algebra sameAs 始代数.
- Initial_algebra sameAs m.0bjznt.
- Initial_algebra sameAs Q6034125.
- Initial_algebra sameAs Q6034125.
- Initial_algebra wasDerivedFrom Initial_algebra?oldid=549097379.
- Initial_algebra isPrimaryTopicOf Initial_algebra.