3 papers
math.CT2026
Some Remarks About Integral Categories
Yaroslav Kopylov, Max Zinchenko
We consider integral categories, a class of categories that gained importance in the last three decades in the categorical foundations of algebra and functional analysis. We discus…
math.CT2025
Some Properties of Homology and Exactness of Nomura's Homology Sequences in a Grandis Homological Category
Yaroslav Kopylov, Vadim Leshkov
We consider Lambek's invariants and for commutative squares in Grandis homological categories. We prove that Nomura's null sequences exist in such categori…
math.DG2025
Some Poincaré--Sobolev inequalities for differential forms
Vladimir Gol'dshtein, Yaroslav Kopylov, Roman Panenko
We continue the~study of embeddings between different classes of Sobolev spaces of differential forms started in 2006 in a~paper by Goldshtein and Troyanov. As in this paper, ou…