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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.
In mathematics, in the area of category theory, a forgetful functor (also known as a stripping functor) 'forgets' or drops some or all of the input's structure or properties 'before' mapping to the output. For an algebraic structure of a given signature, this may be expressed by curtailing the signature: the new signature is an edited form of ...
The Parable of the Faithful Servant (or Parable of the Door Keeper) is a parable of Jesus found in Matthew 24:42-51, Mark 13:34-37, and Luke 12:35-48 about how it is important for the faithful to keep watch. In Matthew's Gospel, it immediately precedes the Parable of the Ten Virgins, which has a similar eschatological theme of being prepared ...
— John 3:16, NIV The Law and the Gospel by Lucas Cranach the Elder (1529); Moses and Elijah point the sinner to Jesus for salvation. Paul the Apostle, like Jews and Roman pagans of his time, believed that sacrifice can bring about new kinship ties, purity, and eternal life. For Paul, the necessary sacrifice was the death of Jesus: Gentiles who are "Christ's" are, like Israel, descendants of ...
The song was released in March 1999, becoming a minor hit in the US. A second release in October 2003 gained the song wider international success. "Be Faithful" topped the charts in Ireland and the United Kingdom in 2003, and peaked within the top 10 of the charts in Australia and Denmark. The song was featured in the trailer for the film The ...
Mitchell's embedding theorem, also known as the Freyd–Mitchell theorem or the full embedding theorem, is a result about abelian categories; it essentially states that these categories, while rather abstractly defined, are in fact concrete categories of modules. This allows one to use element-wise diagram chasing proofs in these categories.
1751. "O Come, All Ye Faithful", also known as "Adeste Fideles", is a Christmas carolthat has been attributed to various authors, including John Francis Wade(1711–1786), John Reading(1645–1692), King John IV of Portugal(1604–1656), and anonymous Cistercianmonks. The earliest printed version is in a book published by Wade.
Faithful amplification. In electronics, faithful amplification is the amplification of a signal, particularly a weak one, by a triode or a transistor such that the signal changes in amplitude but not in shape. [1] [2] [3] In order to achieve this with a bipolar transistor, the transistor is biased. [1] [3] Faithful amplification can only occur ...