Description - Relative Category Theory and Geometric Morphisms by Jonathan Chapman
Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos which allows a topos to be regarded as a category of sets. This enables a fruitful interplay between category theory and set theory. However, one stumbling block to a logical approach to topos theory has been the treatment of geometric morphisms. This book presents a convenient
and natural solution to this problem by developing the notion of a frame relative to an elementary topos. The authors show how this technique enables a logical approach to be taken to topics such as
category theory relative to a topos and the relative Giraud theorem. The work is essentially self-contained except that the authors presuppose a familiarity with basic category theory and topos theory.
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An Oration Delivered Before the Citizens of Boston on the Sixty First Anniversary of American Independence: July 4, 1837.
