Extending Pirashvili’s work, we characterize small additive categories A such that the inclusion in the category of functors from A to abelian groups of the full subcategory of analytic functors induces an isomorphism between extension groups.

We show that for a given exact category, there exists bijection between semibricks (pairwise Hom-orthogonal set of bricks) and length wide subcategories (exact extension-closed abelian subcategories). In particular, we category is if only simple objects form semibrick, is, the Schur's lemma holds.

Abstract We give some characterizations of commutative objects in a subtractive category and central morphisms regular category. In particular, we show that objects, i.e., internal unitary magmas, are the same as abelian groups analogously, centrality has an alternative description terms so-called “subtractors”

The interpretation by Duskin and Glenn of abelian sheaf cohomology as connected components of a category of torsors is extended to homotopy classes. This is simultaneously an extension of Verdier’s version of Čech cohomology to homotopy.

We construct a surjective homomorphism from Somekawa’s K-group associated to a finite collection of semi-abelian varieties over a perfect field to a corresponding Hom group in Voevodsky’s triangulated category of effective motivic complexes.

We construct an isomorphism from Somekawa’s Kgroup associated to a finite collection of semi-abelian varieties (or more general sheaves) over a perfect field to a corresponding Hom group in Voevodsky’s triangulated category of effective motivic complexes.

Polar decomposition unquestionably provides a notion of factorization in the category of Hilbert spaces. But it does not fit existing categorical notions, mainly because its factors are not closed under composition. We observe that the factors are images of functors. This leads us to consider notions of factorization that emphasize reconstruction of the composite category from the factors. We f...

l-adic Étale Theory Hodge Theory Category of l-adic Abelian category MHR Galois modules of real mixed Hodge strucrures Galois group Hodge Galois group GHod := Gal(Q/Q) Galois group of the category MHR Gal(Q/Q) acts on H∗ et(X,Ql), H∗(X(C),R) has a functorial where X is a variety over Q real mixed Hodge structure étale site ?? Gal(Q/Q) acts on the étale site, and thus ?? on categories of étale s...

A proper short exact sequence 0! A!f B! C ! 0 ð*Þ in the category of locally compact abelian groups is said to be t-pure if fðAÞ is a topologically pure subgroup of B, that is, if

This paper describes the historical background and motivation involved in the discovery (or invention) of Chu categories. In 1975, I began a sabbatical leave at the ETH in Zürich, with the idea of studying duality in categories in some depth. By this, I meant not such things as the duality between Boolean algebras and Stone spaces, nor between compact and discrete abelian groups, but rather sel...