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Convenient affine algebraic varieties. (English) Zbl 0739.18003

A. Frölicher [Lect. Notes Math. 962, 69-81 (1982; Zbl 0498.58004)] defined a Cartesian closed subcategory of the category of vector spaces — called the subcategory of convenient vector spaces — wherein to do differential calculus. A similar treatment of functional analysis is accomplished by L. D. Nel [Contemp. Math. 30, 244-276 (1984; Zbl 0548.46054)].
In a similar spirit, the author constructs the category of convenient affine algebraic varieties, AF. Since AF is Cartesian closed the author anticipates that AF will become a public convenience suitable for performing a number of important quotient operations.

MSC:

18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
14A99 Foundations of algebraic geometry
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References:

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