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

Polimetrica, corso Milano 26, Monza (MI). Marie La Palme Reyes, Gonzalo E. Reyes and Houman Zolfaghari

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 develpments. The book is aimed (via appropiate 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.