Mathematics > Algebraic Topology
[Submitted on 25 Nov 2024]
Title:Ephemeral Modules and Scott Sheaves on a Continuous Poset
View PDF HTML (experimental)Abstract:By utilizing domain theory, we generalize the notion of an ephemeral module to the so-called continuous posets. We investigate the quotient category of persistence modules by the Serre subcategory of ephemeral modules and show that it is equivalent to the category of sheaves on the Scott topology. Furthermore, we study the metric properties of persistence modules via this equivalence.
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