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Definitions for
"Monoid"
Keywords:
semigroup
,
algebraic
,
identity
,
element
,
mathematics
a closed half group with a neutral element
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a semigroup that has an identity element
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a semigroup with a unit
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In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element.
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Keywords:
morphisms
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eta
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theory
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abstract
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tend
an abstract model of most situations in which a set of actions tend to change objects
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In category theory, a monoid (or monoid object) (M,\mu,\eta) in a monoidal category C is an object M together with two morphisms
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Keywords:
convex
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analogue
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integer
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rational
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discrete
A set, M, defined on rational vectors, such that: (1) 0 is in M, and (2) if v, w are in M, then v+w is in M. The monoid is integral if it contains only integer vectors. One can think of a monoid as a discrete analogue of a convex cone.
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Keywords:
magma
a magma (M, ), i
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