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Automata and categories

Symeon Bozapalides, Anestis Firarides (1982)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Cartesian closed hull for (quasi-)metric spaces (revisited)

Mark Nauwelaerts (2000)

Commentationes Mathematicae Universitatis Carolinae

An existing description of the cartesian closed topological hull of p MET , the category of extended pseudo-metric spaces and nonexpansive maps, is simplified, and as a result, this hull is shown to be a special instance of a “family” of cartesian closed topological subconstructs of p q s MET , the category of extended pseudo-quasi-semi-metric spaces (also known as quasi-distance spaces) and nonexpansive maps. Furthermore, another special instance of this family yields the cartesian closed topological hull of...

Categorification of Hopf algebras of rooted trees

Joachim Kock (2013)

Open Mathematics

We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H 0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring...

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