Applied Categorical Structures

, Volume 3, Issue 3, pp 239–259 | Cite as

Categories of abstract smooth models and their singular envelopes

  • Martin Jurchescu


We define the categories of (abstract) smooth models (Definition 1.2) and, in the additive case, their singular envelopes (Definition 1.5). The first main result is a relative version of the Yoneda representation theorem (Theorem 1.6), and the second one is an existence and uniqueness theorem for the singular envelope (Theorem 1.7). In fact we prove the existence of a canonical process which associates with each additive smooth-model categoryS a singular envelopeS-an ofS, whose objects are calledS-analytic spaces (Definition 5.1). We notice that most of the fundamental categories of geometry are of the formS-an (up to equivalence). As an application we introduce here two such categories: Banach differentiable spaces and Banach mixed spaces.

Mathematics Subject Classifications (1991)

Primary: 18F99 Secondary 32C15 58B99 

Key words

category over topological spaces functored space Yoneda's representation theorem S-analytic space 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Martin Jurchescu
    • 1
  1. 1.Department of MathematicsBucharest UniversityBucharestRomania

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