Subobject classifier for algebraic structures

Algebraic Structures

Algebraic Structures

In this text, we focus on operations of arity 2, 1, and 0. – For n = 2, f : A → A is a binary operation and is usually written in infix notation, using a binary operation symbol like ·, ∗, or +. Hence, instead of f(a1, a2) we write a1fa2. – For n = 1, f : A→ A is a unary operation. – For n = 0, f : A → A is a nullary operation or a constant. An algebra (or an algebraic structure) is a set A, th...

Algebraic Structures for Spatial Ontologies

The idea of ontology has proven to be an important field of research in geographical information science (Smith and Mark 1998), and it is expected that the use of ontologies will improve interoperability among different geographical databases (Fonseca and Egenhofer 1999). Further advances in the field require abstract specifications of spatial ontologies, to derive useful properties that can be...

Subobject Transformation Systems

Subobject transformation systems (sts) are proposed as a novel formal framework for the analysis of derivations of transformation systems based on the algebraic, double-pushout (dpo) approach. They can be considered as a simplified variant of dpo rewriting, acting in the distributive lattice of subobjects of a given object of an adhesive category. This setting allows for a direct analysis of al...

MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...