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math.AT2024
Magnitude homology and homotopy type of metric fibrations
Yasuhiko Asao, Yu Tajima, Masahiko Yoshinaga
In this article, we show that each two metric fibrations with a common base and a common fiber have isomorphic magnitude homology, and even more, the same magnitude homotopy type.…
math.AT2024
Minimal projective resolution and magnitude homology of geodetic metric spaces
Yasuhiko Asao, Shun Wakatsuki
Asao-Ivanov showed that magnitude homology is a Tor functor, hence we can compute it by giving a projective resolution of a certain module. In this article, we compute magnitude ho…
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…