A survey by Castillo lists results on the category of Banach spaces and on Banach space constructions, such as:

  • Existence of limits in Banach spaces or suitable subcategories
  • Demonstrations of adjointness of functors, even where the natural isomorphisms are in a suitable Banach space type category
  • Exactness of functors in Banach space type categories or weaker properties

I would like to know whether such results exist in a different TVS setting, and where to find them if they do.

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    $\begingroup$ What kind of results? Can you be specific for people who wouldn't go on to read the full survey? $\endgroup$
    – Amir Sagiv
    Jul 17 '18 at 6:58
  • 1
    $\begingroup$ @AmirSagiv Done. $\endgroup$ Jul 17 '18 at 7:02
  • 1
    $\begingroup$ In Schaefer's book, Topological Vector Spaces, sections II.5-II.8 deal with limits and colimits in locally convex spaces and facts such as every complete locally convex space being a directed limit of Banach spaces, and every bornological space being a directed colimit of normed spaces. The terminology is old-fashioned, however, and category theory is not used directly. $\endgroup$ Jul 17 '18 at 12:22
  • 2
    $\begingroup$ The monograph Derived functors in functional analysis (Springer, 2003) by Jochen Wengenroth might be of use. $\endgroup$ Jul 17 '18 at 12:26

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