Handbook of Categorical Algebra: Volume 3, Sheaf Theory

Handbook of Categorical Algebra: Volume 3, Sheaf Theory offers an in-depth exploration of some of the fundamental concepts in category theory, presented with an eye toward clarity and thoroughness. Designed as both a detailed reference for specialists and a comprehensive introduction for users of category theory, this volume extends the series’ goal of equipping researchers with a clear understanding of the vital elements that underlie the subject. In this volume, the treatment begins with a careful study of locales, setting the stage for a systematic examination of sheaves on a locale and on a topological space through various equivalent formulations such as functors, etale maps, and W-sets. The discussion then broadens to include sheaves on a site, with the corresponding concept of a Grothendieck topos introduced in a natural progression. Further, the text investigates the interplay between Grothendieck toposes and the theory of accessible categories and sketches, culminating in a proof of the existence of a classifying topos for all coherent theories.