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A faithful functor need not be injective on objects or morphisms. That is, two objects X and X′ may map to the same object in D (which is why the range of a full and faithful functor is not necessarily isomorphic to C), and two morphisms f : X → Y and f′ : X′ → Y′ (with different domains/codomains) may map to the same morphism in D.
The Cure are an English rock band formed in 1978 in Crawley, West Sussex. [1] [2] [3] Throughout numerous lineup changes since the band's formation, guitarist, lead vocalist, and songwriter Robert Smith has remained the only constant member, though bassist Simon Gallup has been present for all but about three years of the band's history.
The Dark Tower is a 2017 American neo-Western science fantasy film [4] directed and co-written by Nikolaj Arcel.Based on Stephen King's novel series of the same name, the film stars Idris Elba as Roland Deschain, a gunslinger on a quest to protect the Dark Tower—a mythical structure which supports all realities—while Matthew McConaughey plays his nemesis Walter Padick (The Man in Black ...
$1.8 million [2] [3] Fire of Love is a 2022 independent [ 4 ] documentary film about the lives and careers of volcanologists Katia and Maurice Krafft . [ 5 ] Directed, written, and produced by Sara Dosa , the film had its world premiere at the 2022 Sundance Film Festival on January 20, 2022, where it won the Jonathan Oppenheim Editing Award.
Plancherel's theorem makes it possible to extend the Fourier transform, by a continuity argument, to a unitary operator on L 2 (R). On L 1 (R) ∩ L 2 (R), this extension agrees with original Fourier transform defined on L 1 (R), thus enlarging the domain of the Fourier transform to L 1 (R) + L 2 (R) (and consequently to L p (R) for 1 ≤ p ≤ 2).
The kinetic energy of a 2 kg mass travelling at 1 m/s, or a 1 kg mass travelling at 1.41 m/s. The energy required to lift an apple up 1 m, assuming the apple has a mass of 101.97 g. The heat required to raise the temperature of 0.239 g of water from 0 °C to 1 °C. [15] The kinetic energy of a 50 kg human moving very slowly (0.2 m/s or 0.72 km/h).
As Hammer's friend, Sanders appeared in the "2 Legit 2 Quit" music video, and his alter-ego "Prime Time" showed up in Hammer's "Pumps and a Bump" music video. Hammer, being a big sports fan, launched a new enterprise called Roll Wit It Entertainment & Sports Management which boasted such clients as Evander Holyfield , Deion Sanders and Reggie ...