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Wyszukujesz frazę "symmetric monoidal category" wg kryterium: Temat


Wyświetlanie 1-4 z 4
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
Artykuł
Tytuł:
Adjointness between theories and strict theories
Autorzy:
Vogel, Hans-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/728926.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
symmetric monoidal category
dhts-category
partial theory
adjoint functor
Opis:
The categorical concept of a theory for algebras of a given type was foundet by Lawvere in 1963 (see [8]). Hoehnke extended this concept to partial heterogenous algebras in 1976 (see [5]). A partial theory is a dhts-category such that the object class forms a free algebra of type (2,0,0) freely generated by a nonempty set J in the variety determined by the identities ox ≈ o and xo ≈ o, where o and i are the elements selected by the 0-ary operation symbols.
If the object class of a dhts-category forms even a monoid with unit element I and zero element O, then one has a strict partial theory.
In this paper is shown that every J-sorted partial theory corresponds in a natural manner to a J-sorted strict partial theory via a strongly d-monoidal functor. Moreover, there is a pair of adjoint functors between the category of all J-sorted theories and the category of all corresponding J-sorted strict theories.
This investigation needs an axiomatic characterization of the fundamental properties of the category Par of all partial function between arbitrary sets and this characterization leads to the concept of dhts- and dhth∇s-categories, respectively (see [5], [11], [13]).
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 163-212
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Categories of functors between categories with partial morphisms
Autorzy:
Vogel, Hans-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/729097.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
symmetric monoidal category
dhts-category
Hoehnke category
Hoehnke theory
monoidal functor
d-monoidal functor
dht-symmetric functor
functor composition
cartesian product
Opis:
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.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 1; 39-87
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A categorical model of predicate linear logic
Autorzy:
Demeterová, E.
Mihályi, D.
Novitzká, V.
Powiązania:
https://bibliotekanauki.pl/articles/122570.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
linear type theory
predicate linear logic
symmetric monoidal closed category
Opis:
Linear logic is one of the logical systems with special properties suitable for describing real processes used in computer science. It enables one to specify dynamics, non determinism, consecutive processes and important resources as memory and time on syntactic level. Moreover, its deduction system enables one to verify specified properties. Constructing an appropriate model based on categories can serve for modeling various program systems in the wide spectrum of computer science. Mainly, propositional linear logic is used for these purposes. The expression power of linear logic significantly grows by extending propositional logic with predicates and quantifiers. Our paper concerns itself with defining predicate linear logic together with its deduction system and our main aim is to construct a categorical model of predicate linear logic as a symmetric monoidal closed category.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 1; 27-42
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-4 z 4

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