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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That hurt tech stocks. For the past few weeks, the 10-year yield has traded between 1.72% and 2%, as traders moved into the bond for safety when Russia headlines were ugly—and out of it when headlines improved. Now, the yield is touching its pandemic-era high. If the yield breaks above that level, that could signal that it’s on a sustainable path higher. Higher long-dated bond yields make future profits less valuable—and many tech companies are valued on the basis of profits forecast for many years in the future. Two days after Russia invaded Ukraine, an account on the Telegram messaging platform posing as President Volodymyr Zelenskiy urged his armed forces to surrender. So, uh, whenever I hear about Telegram, it’s always in relation to something bad. What gives? You may recall that, back when Facebook started changing WhatsApp’s terms of service, a number of news outlets reported on, and even recommended, switching to Telegram. Pavel Durov even said that users should delete WhatsApp “unless you are cool with all of your photos and messages becoming public one day.” But Telegram can’t be described as a more-secure version of WhatsApp. "The inflation fire was already hot and now with war-driven inflation added to the mix, it will grow even hotter, setting off a scramble by the world’s central banks to pull back their stimulus earlier than expected," Chris Rupkey, chief economist at FWDBONDS, wrote in an email. "A spike in inflation rates has preceded economic recessions historically and this time prices have soared to levels that once again pose a threat to growth."
from fr
