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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.KT2024
Magnitude homology is a derived functor
Yasuhiko Asao, Sergei O. Ivanov
We prove that the magnitude (co)homology of an enriched category can, under some technical assumptions, be described in terms of derived functors between certain abelian categories…
math.KT2023
Transfinite version of the Mittag-Leffler condition for the vanishing of the derived limit
Mishel Carelli, Sergei O. Ivanov
We give a necessary and sufficient condition for an inverse sequence indexed by natural numbers to have . This condition can b…