thinking about how to make homotopical sense of local triviality again...
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local triviality is the point-set condition you need to make point-set stuff floppy enough to be homotopical. from a purely homotopical view i guess you could say everything is already “locally trivial” in the sense that all bundles trivialize over “points”
keep saying smart words and you're gonna make me homotopical 😏
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this is close (maybe dual) to how i am thinking: if i have a nice cech cover with contractible pieces then i can use that to present the homotopy type of my space (the nerve!) and if the structure im trynna classify is homotopy invariant then it better play nice with this.
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but ultimately im interested in looking at things over other grothendieck topologies where stuff is way more rigid, and i'm not sure i can port this over cleanly...
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