Geodesic
On generalized Hom-functors of certain symmetric monoidal categories
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 47-71

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It is well-known that for each object A of any category C there is the covariant functor H^A: C → Set, where H^A(X) is the set C[A,X] of all morphisms out of A into X in C for an arbitrary object X ∈ |C| and H^A(φ), φ ∈ C[X,Y], is the total function from C[A,X] into C[A,Y] defined by C[A,X] ∋ u → uφ ∈ C[A,Y].
Keywords: symmetric monoidal category, monoidal functor, Hom-functor 
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Vogel, Hans. On generalized Hom-functors of certain symmetric monoidal categories. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 47-71. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a4/