Resumen de The hitchhiker guide to categorical Banach space theory. Part I.

Jesús María Fernández Castillo

• What has category theory to offer to Banach spacers? In this survey-like paper we will focus on some of the five basic elements of category theory �namely, i) The definition of category, functor and natural transformation; ii) Limits and colimits; iii) Adjoint functors;

  plus a naive presentation of Kan extensions� to support the simplest answer �tools that work and a point of view that helps to understand problems, even if one does not care at all about categories�. Homology will be treated in a second part.