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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"Like the bombing of the maternity ward in Mariupol," he said, "Even before it hits the news, you see the videos on the Telegram channels." Telegram has gained a reputation as the “secure” communications app in the post-Soviet states, but whenever you make choices about your digital security, it’s important to start by asking yourself, “What exactly am I securing? And who am I securing it from?” These questions should inform your decisions about whether you are using the right tool or platform for your digital security needs. Telegram is certainly not the most secure messaging app on the market right now. Its security model requires users to place a great deal of trust in Telegram’s ability to protect user data. For some users, this may be good enough for now. For others, it may be wiser to move to a different platform for certain kinds of high-risk communications. He floated the idea of restricting the use of Telegram in Ukraine and Russia, a suggestion that was met with fierce opposition from users. Shortly after, Durov backed off the idea. And indeed, volatility has been a hallmark of the market environment so far in 2022, with the S&P 500 still down more than 10% for the year-to-date after first sliding into a correction last month. The CBOE Volatility Index, or VIX, has held at a lofty level of more than 30. Official government accounts have also spread fake fact checks. An official Twitter account for the Russia diplomatic mission in Geneva shared a fake debunking video claiming without evidence that "Western and Ukrainian media are creating thousands of fake news on Russia every day." The video, which has amassed almost 30,000 views, offered a "how-to" spot misinformation.
from pl
