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What (who) is cut homomorphism - definition
![surjective]].](https://commons.wikimedia.org/wiki/Special:FilePath/Exponentiation as monoid homomorphism svg.svg?width=200 "surjective]].")
.jpg?width=200 "Contemporary Czech cut glass in two colours")
.gif?width=200 "Czech glass-cutter at work")
![Chandelier in the chapel of [[Emmanuel College, Cambridge]], donated in 1732, one of the earliest datable cut glass examples. The shape follows contemporary brass examples, with glass branches but no "drops"; only the pieces down the stem are cut, mostly with flat facets.<ref>Battie & Cottle, 102</ref>](https://commons.wikimedia.org/wiki/Special:FilePath/Emmanuel College Chapel 2, Cambridge, UK - Diliff (cropped).jpg?width=200 "Chandelier in the chapel of [[Emmanuel College, Cambridge]], donated in 1732, one of the earliest datable cut glass examples. The shape follows contemporary brass examples, with glass branches but no \"drops\"; only the pieces down the stem are cut, mostly with flat facets.<ref>Battie & Cottle, 102</ref>")
![American "brilliant cut" [[punch bowl]] on stand, 1895](https://commons.wikimedia.org/wiki/Special:FilePath/Punch Bowl on Stand LACMA M.91.320.6.jpg?width=200 "American \"brilliant cut\" [[punch bowl]] on stand, 1895")
![Montgolfier]]" shape (due to its resemblance to an inverted [[hot air balloon]]),<ref>History</ref> in [[Edinburgh]]](https://commons.wikimedia.org/wiki/Special:FilePath/Royal Lyceum Edinburgh Chandelier.jpg?width=200 "Montgolfier]]\" shape (due to its resemblance to an inverted [[hot air balloon]]),<ref>History</ref> in [[Edinburgh]]")
![Regency]] chandeliers in [[Saltram House]], England](https://commons.wikimedia.org/wiki/Special:FilePath/The Saloon (7279934644).jpg?width=200 "Regency]] chandeliers in [[Saltram House]], England")
![[[Waterford Crystal]] factory in 2001](https://commons.wikimedia.org/wiki/Special:FilePath/Waterford Crystal tour - Quality control - geograph.org.uk - 1636581.jpg?width=200 "[[Waterford Crystal]] factory in 2001")
![engraving]] above, England, late 18th-century](https://commons.wikimedia.org/wiki/Special:FilePath/Wine Rinser (England), 18th century (CH 18464757-2) (cropped).jpg?width=200 "engraving]] above, England, late 18th-century")
, 1760–80 (CH 18621563) (cropped).jpg?width=200 "Dessert glass, England, 1760–80")
.jpg?width=200 "Bowl, 1820–30, English")
, early 19th century (CH 18621221).jpg?width=200 "Irish jug, early 19th century")
, ca. 1835 (CH 18621547) (cropped).jpg?width=200 "English (?) vase, c. 1835")
Wikipedia
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).
Homomorphisms of vector spaces are also called linear maps, and their study is the subject of linear algebra.
The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory.
A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of those can be defined in a way that may be generalized to any class of morphisms.
