- Tytuł:
- On generalized Hom-functors of certain symmetric monoidal categories
- Autorzy:
- Vogel, Hans
- Powiązania:
- https://bibliotekanauki.pl/articles/729029.pdf
- Data publikacji:
- 2002
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
symmetric monoidal category
monoidal functor
Hom-functor - Opis:
-
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. - Źródło:
-
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 1; 47-71
1509-9415 - Pojawia się w:
- Discussiones Mathematicae - General Algebra and Applications
- Dostawca treści:
- Biblioteka Nauki
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