AbstractFor over a decade, two theories have been actively developed: theory of magnitude and magnitude homology of metric spaces, and GLMY-theory of path homology of directed graphs. Recently Asao showed that for the case of directed graphs there is a unified approach to these theories via a spectral sequence which is now known as the magnitude-path spectral sequence. He also introduced a noti...
opos theory is a branch of mathematics, based on category theory, which has connections to both algebraic geometry and mathematical logic. Within mathematical logic it can be used to give alternative, more flexible foundations for all of mathematics, and in particular provides the foundation for subjects such as synthetic differential geometry. More recently, the work of Olivia Caramello has sh...
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