51:. In other words, if coalgebras are thought of as a sort of linear analogue of sets, then the measuring coalgebra is a sort of linear analogue of the set of homomorphisms from
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if it preserves the algebra product and identity (in the coalgebra sense). If we think of the elements of
335:, Mathematical Surveys and Monographs, vol. 168, Providence, RI: American Mathematical Society,
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Sweedler, Moss E. (1968), "The Hopf algebra of an algebra applied to field theory",
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is the algebra of continuous real functions on a compact
Hausdorff space
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399:, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York,
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Hazewinkel, Michiel; Gubareni, Nadiya; Kirichenko, V. V. (2010),
214:. A measuring coalgebra is a universal coalgebra that measures
333:
Algebras, rings and modules. Lie algebras and Hopf algebras
301:. This may be the origin of the term "measuring coalgebra".
312:, the measuring coalgebra has a natural structure of a
289:
is the real numbers, then the measuring coalgebra from
297:
can be identified with finitely supported measures on
239:
The group-like elements of a measuring coalgebra from
258:
The primitive elements of a measuring coalgebra from
222:in the sense that any coalgebra that measures
230:can be mapped to it in a unique natural way.
8:
71:. Measuring coalgebras were introduced by
316:, called the Hopf algebra of the algebra
63:are (essentially) the homomorphisms from
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194:multiplies identities by the counit of
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202:is grouplike this just states that
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379:10.1016/0021-8693(68)90059-8
247:are the homomorphisms from
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393:Sweedler, Moss E. (1969),
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439:Coalgebras
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325:References
87:Definition
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172:) where Σ
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234:Examples
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