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.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…
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…