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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.
Here’s the deal: For years, there’s been a popular theory in behavioral science research that people hit a kind of “happiness plateau” around the $75,000 a year threshold (or around ...
Faith. Faith is confidence or trust in a person, thing, or concept. [ 1] In the context of religion, faith is " belief in God or in the doctrines or teachings of religion". [ 2] According to the Merriam-Webster's Dictionary, faith has multiple definitions, including "something that is believed especially with strong conviction", "complete trust ...
Jimmy Carter 's retirement, currently 43 years, is the longest in American presidential history. Additionally, at age 99, Carter is the oldest of the six living U.S. presidents [ 2] as well as the nation's longest-lived president. [ 8] Barack Obama, at age 63, is the youngest living former president.
Frank Schwab. July 17, 2024 at 10:07 AM. One of the unresolved issues of the NFL offseason took another turn Tuesday when receiver Brandon Aiyuk, unhappy with the lack of a contract extension ...
Machu Picchu is a 15th-century Inca citadel located in the Eastern Cordillera of southern Peru on a 2,430-meter (7,970 ft) mountain ridge. [ 2] Often referred to as the "Lost City of the Incas", it is the most familiar icon of the Inca Empire. It is located in the Machupicchu District within Urubamba Province [ 3] above the Sacred Valley, which ...
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Faithful representation. In mathematics, especially in an area of abstract algebra known as representation theory, a faithful representation ρ of a group G on a vector space V is a linear representation in which different elements g of G are represented by distinct linear mappings ρ(g) . In more abstract language, this means that the group ...