Abstract We study Maurer–Cartan moduli spaces of dg algebras and associated categories show that, while not quasi-isomorphism invariants, they are invariants strong homotopy type, a natural notion that has been studied before. prove, in several different contexts, Schlessinger–Stasheff type theorems comparing the notions gauge equivalence for elements as well their categorified versions. As an ...

This paper concerns a number of diagram categories, namely the partition, planar Brauer, partial Motzkin and Temperley–Lieb categories. If [Formula: see text] denotes any these if is fixed morphism, then an associative operation may be defined on by text]. The resulting semigroup called sandwich semigroup. We conduct thorough investigation semigroups, with emphasis structural combinatorial prop...

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure of F . As a by-product we obtain a concrete expression for the structure...

The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

We work out the theory of fractional isomorphism graphons as a generalization to classical finite graphs. The is given in terms homomorphism densities trees and it characterized distributions on iterated degree measures, Markov operators, weak conditional expectation with respect invariant sub-σ-algebras certain quotients graphons.