We develop an analogue of universal algebra in which generating symbols are interpreted as relations. prove a variety theorem for these relational algebraic theories, we find that their categories models precisely the definable categories. The syntax our theories is string-diagrammatic, and can be seen extension usual term theories.

We present a development of Universal Algebra inside Type Theory, formalized using the proof assistant Coq. We define the notion of a signature and of an algebra over a signature. We use setoids, i.e. types endowed with an arbitrary equivalence relation, as carriers for algebras. In this way it is possible to define the quotient of an algebra by a congruence. Standard constructions over algebra...

Some unexpected properties of the cubic algebra generated by the covariant derivatives of a generic Yang-Mills connection over the (s+ 1)-dimensional pseudo euclidean space are pointed out. This algebra is Gorenstein and Koszul of global dimension 3 but except for s = 1 (i.e. in the 2-dimensional case) where it is the universal enveloping algebra of the Heisenberg Lie algebra and is a cubic Art...

In this paper, we start from this idea that the set of nonzero fuzzy subsets of a fuzzy hyperalgebra can be organized naturally as a universal algebra, and constructing the term functions over this algebra we can deduce some results on fuzzy hyperalgebras from some of the very known properties of the term functions of a universal algebra. Also, we present the form of the generated subfuzzy hype...

The abstract representation-free Algebra of the past century is unable to formalize algebra sameness. A counterexample shows a universal transformation that cannot be representation-free. Then, to define transformations between based universal algebras we must introduce the representations corresponding to the bases, contrary to what was possible in general vector spaces and believed possible i...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra S in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adj...

Incomplete Information research is quite mature when it comes to so called existential nulls, where an existential null is a value stored in the database, representing an unknown object. For some reason universal nulls, that is, values representing all possible objects, have received almost no attention. We remedy the situation in this paper, by showing that a suitable finite representation mec...

The aim of this paper is to explain the bialgebra structure of the positive part of the quantized universal enveloping algebra (Drinfeld-Jimbo quantum group) of type Anusing the Lie algebra theory concepts. Recently has been introduced a generalization of Lie algebras, the basic T -Lie algebras [1]. Using the T -Lie algebra concept some new (we think) quantum groups of type Ancan be constructed...