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On generalized Hom-functors of certain symmetric monoidal categories

100%

Vogel H.

Discussiones Mathematicae - General Algebra and Applications

2002

tom 22

nr 1

47-71

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]. If C̲ is a dts-category, then $H^{A}$ is in a natural manner a d-monoidal functor with respect to $\tilde{H^{A}} = $\tilde{H^{A}}⟨X,Y⟩: C[A,X] × C[A,Y] → C[A,X⊗Y]$, $((u₁,u₂) ↦ d_{A}(u₁⊗u₂)) | X,Y ∈ |C|)$ and $i_{H^{A}}:{∅} → C[A,I], (∅ ↦ t_{A})$. This construction can be generalized to functors $H^{e}$ from any dhth∇s-category K̲ into the category P̲a̲r̲ related to arbitrary subidentities e of K̲ (cf. S [3]). Each such generalized Hom-functor $H^{e}$ related to any subidentity $e ≤ 1_{A}$, $o_{A,A} ≠ e$, turns out to be a monoidal dhth∇s-functor from K̲ into P̲a̲r̲.

Categories of functors between categories with partial morphisms

63%

Vogel H.-J.

Discussiones Mathematicae - General Algebra and Applications

2005

tom 25

nr 1

39-87

It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

1 Vogel H.

1 Vogel H.-J.

1 2005

1 2002

Wyniki wyszukiwania

On generalized Hom-functors of certain symmetric monoidal categories

Categories of functors between categories with partial morphisms