This book studies the universal constructions and properties in
categories of commutative algebras, bringing out the specific
properties that make commutative algebra and algebraic geometry
work. Two universal constructions are presented and used here for
the first time. The author shows that the concepts and
constructions arising in commutative algebra and algebraic geometry
are not bound so tightly to the absolute universe of rings, but
possess a universality that is independent of them and can be
interpreted in various categories of discourse. This brings new
flexibility to classical commutative algebra and affords the
possibility of extending the domain of validity and the application
of the vast number of results obtained in classical commutative
algebra. This innovative and original work will interest
mathematicians in a range of specialities, including algebraists,
categoricians, and algebraic geometers.
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