The cartesian closed bicategory of generalised species of structures

Nicola Gambino, Nicola Gambino, Winskel, Hyland, Fiore

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)203-220
Number of pages17
JournalJournal of the London Mathematical Society
Publication statusPublished - 2008

All Science Journal Classification (ASJC) codes

  • General Mathematics


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