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Applied Categorical Structures

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

Categories of abstract smooth models and their singular envelopes

  • Martin Jurchescu
Article
  • 25 Downloads

Abstract

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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References

  1. 1.
    Ceterchi, R.: A localization theorem for topological categories,Stud. Cerc. Mat. 42(1) (1990) 3–8.Google Scholar
  2. 2.
    Douady, A.: Le problème des modules pour les sous-espaces, analytiques d'un espace analytique donné,Ann. Inst. Fourier 16 (1966), 1–95.Google Scholar
  3. 3.
    Feit, P.: Axiomization of passage from “local” structure to global “object”,Mem. Amer. Math. Soc. 101(485) (1993).Google Scholar
  4. 4.
    Grothendieck, A.: Exposés 9–10 in Séminaire H. Cartan 1960/61 (Familles d'espaces complexes et fondements de la géométrie analytique).Google Scholar
  5. 5.
    Jurchescu, M.: Espaces mixtes, inSpringer Lect. Notes in Math. 1014, 1983, pp. 37–57.Google Scholar
  6. 6.
    Jurchescu, M.: Categories of abstract smooth models and geometric categories, 92/19, Preprint Dipartimento di Matematica “Guido Castelnuovo”, Roma.Google Scholar
  7. 7.
    Reichard, V.: Nicht differenzierbare morphismen differenzierbarer Räume,Manuscripta Math. 15 (1975), 243–250.Google Scholar
  8. 8.
    Serre, J.-P.: Faisceaux algébriques cohérents,Ann. of Math. 61 (1955), 197–278.Google Scholar
  9. 9.
    Spallek, K.: Differenzierbare Räume,Math. Ann. 180 (1969), 269–296.Google Scholar
  10. 10.
    Yoneda, N.: On the homology theory of modules,J. Fac. Sci. Tokyo 54 (1954), 193–227.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

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

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