Quasi-abelian categories are abundant in functional analysis and representation theory. It is known that a quasi-abelian category $\mathcal{E}$ cotilting torsionfree class of an abelian category. In fact, this property characterizes categories. This ambient derived equivalent to the $\mathcal{E}$, can be constructed as heart $\mathcal{LH}(\mathcal{E})$ $t$-structure on bounded $\mathbf{D}^b(\ma...

Every smooth manifold contains particles which propagate. These form objects and morphisms of a category equipped with a functor to the category of Abelian groups, turning this into a 0 + 1 topological field theory. We investigate the algebraic structure of this category, intimately related to the structure of Stasheff’s polytops, introducing the notion of associahedral categories. An associahe...

We give a classification of substructures (= closed subbifunctors) given skeletally small extriangulated category by using the defects, in similar way to author’s exact structures additive category. More precisely, for an category, possible are bijection with Serre subcategories abelian consisting defects conflations. As byproduct, we prove that poset on it is isomorphic some

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...

Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

Introduction. The notion of an additive category was abstracted from the example of all modules over a ring, a very large category. However with tongue firmly in cheek, one can define a ring with identity (all rings will have identity) as an additive category with just one object. Years ago, the notion of a Morita context was expounded with a certain amount of labour. A Morita context turned ou...

Bivariant (equivariant) K-theory is the standard setting for noncommutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from homological algebra: phantom maps, exact chain complexes, projective resolutions, and derived functors. We introduce these notions and apply them to examples from bivar...