论文信息 - Generalised Species of Structures : Cartesian Closed and Differential Structure ( Working Draft )

Generalised Species of Structures : Cartesian Closed and Differential Structure ( Working Draft )

We generalise Joyal’s notion of species of structures and develop their combinatorial calculus. In particular, we provide operations for their composition, addition, multiplication, pairing and projection, abstraction and evaluation, and differentiation; developing both the cartesian closed and linear structures of species.

Marcelo Fiore | M. Fiore

[1] G. M. Kelly,et al. A universal property of the convolution monoidal structure , 1986 .

[2] Gilbert Labelle,et al. Combinatorial species and tree-like structures , 1997, Encyclopedia of mathematics and its applications.

[3] Gian-Carlo Rota,et al. Plethysm, categories, and combinatorics , 1985 .

[4] B Jean,et al. Distributors at Work , 2000 .

[5] François Bergeron,et al. Une combinatoire du pléthysme , 1987, J. Comb. Theory, Ser. A.

[6] F. William Lawvere,et al. Metric spaces, generalized logic, and closed categories , 1973 .

[7] G. M. Kelly,et al. BASIC CONCEPTS OF ENRICHED CATEGORY THEORY , 2022, Elements of ∞-Category Theory.

[8] Miguel A. Méndez,et al. Colored Species, c-Monoids, and Plethysm, I , 1993, J. Comb. Theory, Ser. A.

[9] A. Joyal. Une théorie combinatoire des séries formelles , 1981 .

[10] B. Day. On closed categories of functors , 1970 .

[11] Miguel A. Méndez. Species on Digraphs , 1996 .

[12] Laurent Regnier,et al. The differential lambda-calculus , 2003, Theor. Comput. Sci..

[13] J. Benabou. Introduction to bicategories , 1967 .