The cartesian closed bicategory of generalised species of structures

Nicola Gambino, Nicola Gambino, Winskel, Hyland, Fiore

Risultato della ricerca: Article

29 Citazioni (Scopus)

Abstract

The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These definitions encompass most notions of combinatorial species considered in the literature - including of course Joyal's original notion - together with their associated substitution operation. Our first main result exhibits the substitution calculus of generalised species as arising from a Kleisli bicategory for a pseudo-comonad on profunctors. Our second main result establishes that the bicategory of generalised species of structures is cartesian closed.
Lingua originaleEnglish
pagine (da-a)203-220
Numero di pagine17
RivistaJournal of the London Mathematical Society
Volume2008
Stato di pubblicazionePublished - 2008

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Bicategory
Cartesian
Closed
Substitution
Functor
Presheaves
Calculus

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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The cartesian closed bicategory of generalised species of structures. / Gambino, Nicola; Gambino, Nicola; Winskel; Hyland; Fiore.

In: Journal of the London Mathematical Society, Vol. 2008, 2008, pag. 203-220.

Risultato della ricerca: Article

Gambino, Nicola ; Gambino, Nicola ; Winskel ; Hyland ; Fiore. / The cartesian closed bicategory of generalised species of structures. In: Journal of the London Mathematical Society. 2008 ; Vol. 2008. pagg. 203-220.
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AB - The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These definitions encompass most notions of combinatorial species considered in the literature - including of course Joyal's original notion - together with their associated substitution operation. Our first main result exhibits the substitution calculus of generalised species as arising from a Kleisli bicategory for a pseudo-comonad on profunctors. Our second main result establishes that the bicategory of generalised species of structures is cartesian closed.

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