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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.
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.
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