
Methods and ModelsMethods and Models 27
The functions F[σ] should satisfy the functorial properties:
• For all bijections σ: U →V and τ: V →W, F [τ ◦ σ]: F[τ] ◦F[σ]
• For the identity map Id
U
: U →V, F [Id
U
] = Id
F(U)
The functor F, which produces the structures F [U] and the transport
functions F[σ] can be described in different fashions provided that the
functorial conditions hold.
For example one can use axiomatic systems, constructions, algorithms,
combinatorial operations, functional equations, geometric fi gures to specify
species.
The key to grasp the concept of combinatorial structure in mathematical
terms consists in using the concept ...