(See Theorem 3.23 in Pirkovskii.) The category of Stein spaces of finite embedding dimension is contravariantly equivalent to the category of those finitely generated EFC-algebras defined by closed ideals (holomorphically finitely generated algebras in Pirkovskii’s terminology of Definition 3.16). The equivalence functor sends a Stein space to its EFC-algebra of global sections.

J. P. Pridham, A differential graded model for derived analytic geometry, Advances in Mathematics 360 (2020), 106922. arXiv:1805.08538v1, doi:10.1016/j.aim.2019.106922.

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