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)
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
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Given the pro-privacy stance of the platform, it’s taken as a given that it’ll be used for a number of reasons, not all of them good. And Telegram has been attached to a fair few scandals related to terrorism, sexual exploitation and crime. Back in 2015, Vox described Telegram as “ISIS’ app of choice,” saying that the platform’s real use is the ability to use channels to distribute material to large groups at once. Telegram has acted to remove public channels affiliated with terrorism, but Pavel Durov reiterated that he had no business snooping on private conversations. Telegram boasts 500 million users, who share information individually and in groups in relative security. But Telegram's use as a one-way broadcast channel — which followers can join but not reply to — means content from inauthentic accounts can easily reach large, captive and eager audiences. As a result, the pandemic saw many newcomers to Telegram, including prominent anti-vaccine activists who used the app's hands-off approach to share false information on shots, a study from the Institute for Strategic Dialogue shows. WhatsApp, a rival messaging platform, introduced some measures to counter disinformation when Covid-19 was first sweeping the world. Either way, Durov says that he withdrew his resignation but that he was ousted from his company anyway. Subsequently, control of the company was reportedly handed to oligarchs Alisher Usmanov and Igor Sechin, both allegedly close associates of Russian leader Vladimir Putin.
from fr
