Let be a concrete category and T: S the forgetful functor. If T has
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Let ℓ be a concrete category and T: ℓ → S the forgetful functor. If T has a left adjoint F : S → ℓ, then F is called a free-object functor and F(X) (X ϵ S) is called a free F-object on X.
(a) The category of groups has a free-object functor.
(b) The category of commutative rings with identity and identity preserving homomorphisms has a free-object functor.
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a Yes the category of groups has a freeobject functor Lets denote this category by and the category of groups by S To show that the forgetful functor ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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