Despite of the fact that graph based methods are gaining more and more popularity in different scientific areas, it has to be considered that the choice of an appropriate algorithm for a given application is still the most crucial task. The lack of a large database of graphs makes the task of comparing the performance of different graph matching algorithms difficult, and often the selection of ...

In this short note we construct two families of examples large stratifying systems in module categories algebras. The first consist on infinite size the category an algebra A. second family show that a finite system dimensional A can be arbitrarily comparison to number isomorphism classes simple A-modules. We both are built using well-established results higher homological algebra.

Lenses are a heavily studied form of bidirectional transformation, with diverse applications including database view updating, software development and memory management. Previous work has explored lenses category-theoretically, and established that the category of lenses for a fixed ‘view’ V is, up to isomorphism, the category of algebras for a particular monad on set/V . It has recently been ...

We study finite quasi-quantum groups in their quiver setting developed recently by the first author. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentation type, or equivalently a classification of elementary quasi-Hopf algebras of finite representation type, over the field of complex numbers. By the Tannaka-Krein duality principle, this provides a cl...

The general notion of what is now called Hall algebra or Ringel-Hall algebra is an algebra defined out of a certain type of category, a "finitary abelian category". Finitary abelian categories are, roughly speaking, categories where the notions of exact sequences make sense and such that for any pair of objects A,B in the category in question, we have # Hom(A,B) <∞ and # Ext1(A,B) <∞. The Hall ...

We present a modular correspondence between various categorical structures and their internal languages in terms of extensional dependent type theories à la Martin-Löf. Starting from lex categories, through regular ones we provide internal languages of pretopoi and topoi and some variations of them, like for example Heyting pretopoi. With respect to the internal languages already known for some...

Due to the nature of product in the category of locales, the entourage uniformities in the point-free context only mimic the classical Weil approach while the cover (Tukey type) ones can be viewed as an immediate extension. Nevertheless the resulting categories are concretely isomorphic. We present a transparent construction of this isomorphism, and apply it to the natural uniformities of local...

In this paper, the notion of fuzzy n-polygroups (Fn -polygroups) is introduced and some related properties are investigated. In this regards, the concepts of normal  F-subpolygroups and homomorphisms of Fn-polygroups are adopted. Also, the quotient of Fn-polygroups by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Fn-polygroups p...

It is well known that a measured groupoid G defines a von Neumann algebra W ∗(G), and that a Lie groupoid G canonically defines both a C∗-algebra C∗(G) and a Poisson manifold A∗(G). We construct suitable categories of measured groupoids, Lie groupoids, von Neumann algebras, C∗-algebras, and Poisson manifolds, with the feature that in each case Morita equivalence comes down to isomorphism of obj...