Fibred Categories and the Theory of Structures - (Part I)

Abstract

<p> This THESIS comprises the core of Chapter I and a self-contained excerpt from Chapter II of the author's work "Fibred Categories and the Theory of Structures". As such, it contains a recasting of "categorical algebra" on the (BOURBAKI) set-theoretic frame of GROTHENDIECK-SONNERuniverses, making use of the GROTHENDIECK structural definition of category from the beginning. The principle novelties of the presentation result from the exploitation of an intrinsic construction of the arrow category C^2 of a VL -category C. This construction gives rise to the adjunction of a (canonical) (VL-CAT)-category structure to the couple (C^2, C), for which the consequent category structure supplied the couple (CAT(T,C^2), CAT(T, C)) for each category T, is simply that of natural transformations of functors (which as such are nothing more than functors into the arrow category).</p>