An algebraic category C is called balanced if the cotriple cohomology of any object of C vanishes in positive dimensions on injective coefficient modules. Important examples of balanced and of non-balanced categories occur in the literature. In this paper we prove that the category of crossed modules in groups is non-balanced.

It is proved that in any pointed category with pullbacks, coequalizers and regular epi-mono factorizations, the class of regular epimorphisms is stable under pullback along the so-called balanced effective descent morphisms. Here “balanced” can be omitted if the category is additive. A balanced effective descent morphism is defined as an effective descent morphism p : E → B such that any subobj...

We prove that the existence of arbitrarily large supercompact cardinals implies that every absolute epireflective class of objects in a balanced accessible category is a small-orthogonality class. In other words, if L is a localization functor on a balanced accessible category such that the unit morphism X → LX is an epimorphism for all X and the class of L-local objects is defined by an absolu...

The issue of credit risk and deferred bank claims is one of the sensitive issues of banking industry, which can be considered as the main cause of bank failures. In recent years, the economic slowdown accompanied by inflation in Iran has led to an increase in deferred bank claims that could put the country's banking system in serious trouble. Accordingly, the current paper presents a prediction...

In this paper, we study the behaviour of monomorphisms, epimorphisms, co-retractions and retractions in the category of G-sets. Further, some special objects are discussed here and obtain that the category of G-sets is balanced, well powered and co-well powered.

Abstract. This paper contains the construction, examples and properties of a trace and a trace pairing for certain morphisms in a monoidal category with switching isomorphisms. Our construction of the categorical trace is a common generalization of the trace for endomorphisms of dualizable objects in a balanced monoidal category and the trace of nuclear operators on a topological vector space w...

We study when the stable category A of an abelian category A modulo a full additive subcategory T is balanced and, in case T is functorially finite in A, we study a weak version of balance for A . Precise necessary and sufficient conditions are given in case T is either a Serre class or a class consisting of projective objects. The results in this second case apply very neatly to (gen...

We present a study examining cognitive functions in late non-balanced bilinguals with different levels of second language proficiency. We examined in two experiments a total of 193 mono- and bilingual university students. We assessed different aspects of attention (sustained, selective and attentional switching), verbal fluency (letter and category) as well as picture-word association as a meas...