We extend the concept of graph isomorphisms to multilayer networks, and we identify multiple types of isomorphisms. For example, in multilayer networks with a single “aspect” (i.e., type of layering), permuting vertex labels, layer labels, and both of types of layers each yield a different type of isomorphism. We discuss how multilayer network isomorphisms naturally lead to defining isomorphism...

We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such as the index-group, monoid of automata rules, and its subgroup of reversible elements). However for some groups there exist not regular automata isomorphism...

In 2010, J. Climent Vidal and J. Soliveres Tur developed, among other things, a pair of 2-adjunctions between the 2-category of adjunctions and the 2-category of monads. One is related to the Kleisli adjunction and the other to the Eilenberg-Moore adjunction for a given monad.Since any 2-adjunction induces certain natural isomorphisms of categories, these can be used to classify bijection...

A study of strong sums: isomorphisms and normal forms The goal of this thesis is to study the sum and the zero within two principal frameworks: type isomorphisms and the normalization of λ-terms. Type isomorphisms have already been studied within the framework of the simply typed λ-calculus with surjective pairing but without sums. To handle the case with sums and zero, I first restricted the s...

It is known that isomorphisms of graph Jacobians induce cyclic bijections on the associated graphs. We characterize when such can be strengthened to isomorphisms, in terms an easily computed divisor. The result refines tools used algebraic geometry examine fibers compactified Torelli map.

In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a chain homotopy invariant on the collection of all quasi-isomorphisms from a bas...

In the structure theory of quantized enveloping algebras, the algebra isomorphisms determined by Lusztig led to the first general construction of PBW bases of these algebras. Also, they have important applications to the representation theory of these and related algebras. In the present paper the Drinfel’d double for a class of graded Hopf algebras is investigated. Various quantum algebras, in...

We consider two categories of C-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on them, crop up in a variety of C-algebraic contexts. We show that Rieffel’s construction of a fixed-point algebra for a proper action can be made into functor...

We show that, in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits, and extensions also isomorphisms particular co-reflective. In this way, we extend to group-theoretic framework topological analogue proved by Chach´olski, Parent, Stanley 2004. establish several new relations between classes.