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Homomorphisms of algebras

Miroslav Novotný (2002)

Czechoslovak Mathematical Journal

A construction of all homomorphisms of an algebra with a finite number of operations into an algebra of the same type is presented that consists in replacing algebras by suitable mono-unary algebras (possibly with some nullary operations) and their homomorphisms by suitable homomorphisms of the corresponding mono-unary algebras. Since a construction of all homomorphisms between two mono-unary algebras is known (see, e.g., [6], [7], [8]), a construction of all homomorphisms of an arbitrary algebra...

Homomorphisms of heterogeneous algebras

Miroslav Novotný (2002)

Czechoslovak Mathematical Journal

A construction of all homomorphisms of a heterogeneous algebra into an algebra of the same type is presented. A relational structure is assigned to any heterogeneous algebra, and homomorphisms between these relational structures make it possible to construct homomorphisms between heterogeneous algebras. Homomorphisms of relational structures can be constructed using homomorphisms of algebras that are described in [11].

Information systems in categories of valued relations.

Vladimir B. Gisin (1994)

Mathware and Soft Computing

The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.

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

Hans-Jürgen Vogel (2001)

Discussiones Mathematicae - General Algebra and Applications

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 ∈ | R e l | ) of diagonal morphisms, a family t = ( t A : A → I | A ∈ | R e l | ) of terminal morphisms, and a family ∇ = ( ∇ A : A ⨂ A → A | A ∈ | R e l | ) 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)....

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