3 papers
math.KT2025
Functorial languages in homological algebra and lower central series
Nikita Golub, Vasily Ionin, Lev Mukoseev
There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories…
math.KT2024
On diagonal digraphs, Koszul algebras and triangulations of homology spheres
Sergei O. Ivanov, Lev Mukoseev
We study magnitude homology of digraphs, with a particular focus on diagonal digraphs, i.e., digraphs whose magnitude homology is concentrated on the diagonal. For any digraph ,…
math.AT2024
On the path homology of Cayley digraphs and covering digraphs
Shaobo Di, Sergei O. Ivanov, Lev Mukoseev +1
We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a "bridge" between GLMY-theory and group ho…