Topoi: The Categorial Analysis of Logic
A classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally.
Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The introduction to topos structure covers topos logic, algebra of subobjects, and intuitionism and its logic, advancing to the concept of functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.
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Review: Topoi: The Categorial Analysis of LogicUser Review - Mark Gomer - Goodreads
What Goldblatt lacks in elegance and concision he mostly makes up for in scope. Read full review
Review: Topoi: The Categorial Analysis of LogicUser Review - Nick Black - Goodreads
Well, I wanted to get category theory straight in my head, and with this accomplished that goal...but at what price? A fairly turgid work, but perhaps that's necessary for handling this field. Read full review