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In other words, if we fix a set A, then the functor Set → Set, X 7→ X × A is left adjoint to the functor Set → Set, Y 7→ Hom(A, Y ).
A functor F from C to D assigns to every object X ∈ C an object F (X) ∈ D and to every morphism f ∈ Mor(X, Y ) a morphism F (f ) ∈ Mor(F (X), F (Y )) such that • F (idX ) = idF (X) for all X ∈ C and • F (f ◦ g) = F (f ) ◦ F (g) for any composable morphisms f, g ∈ C.
We present a functor between the category of smooth manifolds equipped with diffeomorphisms (or local diffeomorphisms) and the category of symplectic manifolds equipped with symplectomorphisms for which the object assignment consists of associating to a space its cotangent bundle.
Definition An “n + 1 dimensional topological quantum field theory” (or “topological field theory”) is a symmetric monoidal functor Z :
A pseudouniversal, Boole prime is a functor if it is hyper-null, Germain, sub-multiply pseudo-ordered and globally D´escartes.
“Double case” and “functor fusion” ...............................................................