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.

FIORE, M., GAMBINO, N., HYLAND, M., WINSKEL, G. (2008). The cartesian closed bicategory of generalised species of structures. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 2008, 203-220 [10.1112/jlms/jdm096].

The cartesian closed bicategory of generalised species of structures

GAMBINO, Nicola;
2008-01-01

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.
2008
FIORE, M., GAMBINO, N., HYLAND, M., WINSKEL, G. (2008). The cartesian closed bicategory of generalised species of structures. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 2008, 203-220 [10.1112/jlms/jdm096].
File in questo prodotto:
File Dimensione Formato  
TheCartesianClosedBicategoryOfGeneralisedSpeciesOfStructures.pdf

Solo gestori archvio

Dimensione 284.66 kB
Formato Adobe PDF
284.66 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/40051
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 56
  • ???jsp.display-item.citation.isi??? 51
social impact