Categorical Logic
(278x)
Time and place: MWF 2-3, Science Center 222
Professor: Jacob Lurie
Office: Science Center 514
Office hours: Wednesday 3-4 (or by appointment).
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The
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course
syllabus. |
Lectures (Warning: lecture notes are unpolished. Use at own
risk.):
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Lecture 1:
Overview. |
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Lecture 2:
Syntax. |
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Lecture 3:
Structure of Weak Syntactic Categories. |
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Lecture 4: Coherent Categories. |
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Lecture 5: Booleanization. |
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Lecture 6: Completeness Theorems. |
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Lecture 7: Pretopoi. |
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Lecture 8: Grothendieck Topologies. |
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Lecture 9: Sheaves and Sheafification. |
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Lecture 10: Giraud's Theorem. |
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Lecture 11: Coherent Topoi. |
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Lecture 12: Geometric Morphisms. |
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Lecture 13: Elimination of Imaginaries. |
The direction the course should have gone (maybe after Lecture 14/15):
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Lecture 14X: Pro-Objects. |
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Lecture 15X: Pro-Etale Sheaves. |
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Lecture 16X-Parametrized Models. |
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Lecture 17X-Deligne's Theorem; Filtered Colimits. |
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Lecture 18X-Coverings in Stone_C. |
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Lecture 19X-Sheaves on Stone_C. |
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Lecture 20X-Ultraproducts. |
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Lecture 21X-Characterizing the image of C. |
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Lecture 22X-Embedding into Ultrapowers. |
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Lecture 23X-Compatiblity with Filtered Colimits. |
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Lecture 24X-Ultracategory Fibrations. |
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Lecture 25X-Ultracategories. |
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Lecture 26X-Ultrasets. |
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Lecture 27X-Ultrafunctors. |
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Lecture 28X-Ultrafunctors to Set. |
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Lecture 29X-Makkai Duality. |
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Lecture 30X-Higher Categorical Logic. |
Unfinished story, ultimately not needed:
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Lecture 14: Locales and Topoi. |
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Lecture 15: Spaces and Locales. |
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Lecture 16: Enumerations. |
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Lecture 17: Open Morphisms. |
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Lecture 18: Localic Morphisms. |
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Lecture 19: Reconstruction of Localic Morphisms. |
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Lecture 20-Locales in a topos. |
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