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Is there a reason for ’abelian topological group’ when ’topological abelian group’ exists already? I have only been skimmimg the stuff on condensed mathematics so am not sure if this is like ’presheaf of sets’, a concept ’with attitude’ or not.
Turning analytic geometry into algebraic geometry sounds like making things a lot harder!
Re #2, oh yes, I got confused by the abbreviation AbTop.
Re #3, well Lawvere promises something similar at bornological topos.
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