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This document is a re-writing of the book of Makkai-Reyes with the same title. It is due to Francisco Marmolejo, who not only re-wrote it but made several corrections.

Generic figures and their glueings, A constructive approach to functor categories by

Marie La Palme Reyes, Gonzalo E. Reyes and Houman Zolfaghari. Originally published in 2004 by Polimetrica, corso Milano 26, Monza (MI), but now out of print. The entire book can be found by clicking the link below.

Abstract

This book is a “missing link” between the elementary textbook of Lawvere and Schanuel “Conceptual Mathematics” and the much more advanced textbooks such as MacLane and Moerdijk “Sheaves in Geometry and Logic”. The book introduces (and limits itself) to presheaves toposes, i.e., readily visualizable categories whose objects result from glueing simpler ones, the “generic figures”. Fundamental differences between toposes and the category of sets appear at this level already. Six easy to visualize examples accompany the reader through the whole book, illuminating new material, exemplifying general results and suggesting new developments. The book is aimed (via relevant examples) at a beginner mathematician or scientist or philosopher who would like to take advantage of the richness of presheaf toposes to prepare himself or herself either for further study or applications of the theory described.

Macnamara J. and G. E. Reyes (eds.) (1994). The Logical Foundations of

Cognition. New York: Oxford University Press.

Moerdijk I. and G. E. Reyes (1991). Models for Smooth Infinitesimal Analysis.

New York: Springer-Verlag.

Makkai M. and G. E. Reyes (1977). First-order categorical logic. LNM 611.

Berlin: Springer-Verlag.