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1. • CommentRowNumber1.
   • CommentAuthorNonsensei
   • CommentTimeNov 2nd 2022
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   Author: Nonsensei
   Format: TextHello. I'm new here. I intend to do a PhD and research in category and topos theory. I am looking for guidance on topos theory books. Since topos theory "connects" logic, algebra, and geometry, I am particularly interested in the emphasis of the books. What emphasis, if any, is given in the following three books: geometry, algebra, or logic? - "Sheaves in Geometry and Logic", MacLane and Moerdijk; - "Topos Theory", Johnstone (the Dover book, not the compendium); - "Handbook of Categorical Algebra Vol. 3", Borceux. Thank you in advance for your help.

   Hello.
   
   I'm new here. I intend to do a PhD and research in category and topos theory. I am looking for guidance on topos theory books. Since topos theory "connects" logic, algebra, and geometry, I am particularly interested in the emphasis of the books. What emphasis, if any, is given in the following three books: geometry, algebra, or logic?
   - "Sheaves in Geometry and Logic", MacLane and Moerdijk;
   - "Topos Theory", Johnstone (the Dover book, not the compendium);
   - "Handbook of Categorical Algebra Vol. 3", Borceux.
   
   Thank you in advance for your help.
2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeNov 2nd 2022
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   Author: Dmitri Pavlov
   Format: MarkdownItexMac Lane–Moerdijk: mostly geometry, some logic Johnstone: mostly logic, some geometry Borceux: mostly logic, some geometry The classifying topos (i.e., “algebra”) is considered in all three books.

   Mac Lane–Moerdijk: mostly geometry, some logic

   Johnstone: mostly logic, some geometry

   Borceux: mostly logic, some geometry

   The classifying topos (i.e., “algebra”) is considered in all three books.

3. • CommentRowNumber3.
   • CommentAuthorNonsensei
   • CommentTimeNov 13th 2022
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   Author: Nonsensei
   Format: TextFrom what I gather, "Theories, Sites, Toposes" by Caramello, is predominantly logic (correct me if I'm wrong). If that's the case, would it be a good idea to study "Sheaves in Geometry and Logic", and then study "Theories, Sites, Toposes", to get a well rounded understanding of topos theory?

   From what I gather, "Theories, Sites, Toposes" by Caramello, is predominantly logic (correct me if I'm wrong). If that's the case, would it be a good idea to study "Sheaves in Geometry and Logic", and then study "Theories, Sites, Toposes", to get a well rounded understanding of topos theory?
4. • CommentRowNumber4.
   • CommentAuthorDmitri Pavlov
   • CommentTimeNov 13th 2022
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   Author: Dmitri Pavlov
   Format: MarkdownItexCaramello's book is mostly (universal) algebra, with some logic and geometry. (In particular, sites are emphasized in her book.) > If that's the case, would it be a good idea to study "Sheaves in Geometry and Logic", and then study "Theories, Sites, Toposes", to get a well rounded understanding of topos theory? Well-rounded for what purpose? There are plenty of aspects not covered in either book: anything relating topos theory and homotopy theory, anything about computability (e.g., realizability toposes), synthetic differential geometry, etc.

   Caramello’s book is mostly (universal) algebra, with some logic and geometry. (In particular, sites are emphasized in her book.)

   If that’s the case, would it be a good idea to study “Sheaves in Geometry and Logic”, and then study “Theories, Sites, Toposes”, to get a well rounded understanding of topos theory?

   Well-rounded for what purpose? There are plenty of aspects not covered in either book: anything relating topos theory and homotopy theory, anything about computability (e.g., realizability toposes), synthetic differential geometry, etc.

5. • CommentRowNumber5.
   • CommentAuthorNonsensei
   • CommentTimeNov 14th 2022
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   Author: Nonsensei
   Format: TextI meant well rounded in the sense of learning the whole field. Within reason, of course. I don't mean learning literally everything about topos theory, but every important thing. Anyway, thank you for your replies, they clarified what I wanted to know.

   I meant well rounded in the sense of learning the whole field. Within reason, of course. I don't mean learning literally everything about topos theory, but every important thing. Anyway, thank you for your replies, they clarified what I wanted to know.