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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.
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While representations of G over a field K are de facto the same as K[G]-modules (with K[G] denoting the group algebra of the group G), a faithful representation of G is not necessarily a faithful module for the group algebra. In fact each faithful K[G]-module is a faithful representation of G, but the converse does not hold.
Its etymology is distantly related to that of fidelity; indeed, in modern electronic devices, a machine with high "fidelity" is considered "faithful" to its source material. [ citation needed ] Similarly, a spouse who, inside a sexually exclusive relationship, has sexual relations outside of marriage could be considered as being "unfaithful ...
Faithful is the seventh studio album by American musician Todd Rundgren, released in May 1976 on Bearsville Records. Music. Rundgren explained the motivation of the ...
Faithful is a 1996 American comedy crime drama film directed by Paul Mazursky and starring Cher, Chazz Palminteri and Ryan O'Neal. Palminteri wrote the screenplay, which is an adaptation of his stage play of the same name.
Faithful is the seventh album recorded by Dusty Springfield and was her planned third album for Atlantic Records, recorded in the first half of 1971. In April 2015, Faithful was released as her fifteenth and final studio album (on 7 April in the US and 13 April in the UK), 44 years after its planned release was shelved.
A 1-bit DAC (sometimes called Bitstream converter by Philips) is a consumer electronics marketing term describing an oversampling digital-to-analog converter (DAC) that uses a digital noise shaping delta-sigma modulator operating at many multiples of the sampling frequency that outputs to an actual 1-bit DAC (which could be fully differential to minimize crosstalk). [1]