Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: subidentity

Sortuj według:

Ogranicz wyniki do:

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions

100%

Vogel H.-J.

Discussiones Mathematicae - General Algebra and Applications

2001

tom 21

nr 2

139-163

The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family $d = (d_{A}: A → A⨂ A | A ∈ |Rel|)$ of diagonal morphisms, a family $t = (t_{A}: A → I | A ∈ |Rel|)$ of terminal morphisms, and a family $∇ = (∇_{A}: A ⨂ A → A | A ∈ |Rel|)$ of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category). Besides of certain identities this system of axioms contains two identical implications. In this paper is shown that there is an equivalent characterizing system of axioms for hdht∇s-categories consisting of identities only. Therefore, the class of all small hdht∇-symmetric categories (interpreted as hetrogeneous algebras of a certain type) forms a variety and hence there are free theories for relational structures.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Vogel H.-J.

1 2001

Wyniki wyszukiwania

On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions