сладко стянул

3. (Интригующее заявление, что в итоге теорию гомотопий можно запрятать в обычные группоиды + категорию чумов)

It is perhaps instructive to mention how our theory describes homotopy
types. These correspond to enhanced groupoids, that is, enhanced categories given by fibrations C→Pos+ whose fibers are groupoids. In a sense, the whole gadget exhibits a sort of an Eckmann-Hilton duality between the ideas of order (exemplified by partially ordered sets J ∈ Pos+) and symmetry (exemplified by the groupoids C_J). In another sense, it restores the original idea of “symmetries between symmetries”, but in different guise. There are no “higher groupoids”, there are just groupoids in the usual sense – but a whole bunch of them (just as a scheme can be thought of as a bunch of sets of its points over various affine schemes)

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2.0K viewsedited  Oct 1, 2024 at 07:24

3. (Интригующее заявление, что в итоге теорию гомотопий можно запрятать в обычные группоиды + категорию чумов)

It is perhaps instructive to mention how our theory describes homotopy
types. These correspond to enhanced groupoids, that is, enhanced categories given by fibrations C→Pos+ whose fibers are groupoids. In a sense, the whole gadget exhibits a sort of an Eckmann-Hilton duality between the ideas of order (exemplified by partially ordered sets J ∈ Pos+) and symmetry (exemplified by the groupoids C_J). In another sense, it restores the original idea of “symmetries between symmetries”, but in different guise. There are no “higher groupoids”, there are just groupoids in the usual sense – but a whole bunch of them (just as a scheme can be thought of as a bunch of sets of its points over various affine schemes)

BY сладко стянул