**Time and place:** MWF 2-3, Science Center 222

**Professor:** Jacob Lurie

**Office:** Science Center 514

**Office hours:** Wednesday 3-4 (or by appointment).

The
course
syllabus.

**Lectures (Warning: lecture notes are unpolished. Use at own
risk.)**:

Lecture 3: Structure of Weak Syntactic Categories.

Lecture 4: Coherent Categories.

Lecture 6: Completeness Theorems.

Lecture 8: Grothendieck Topologies.

Lecture 9: Sheaves and Sheafification.

Lecture 12: Geometric Morphisms.

Lecture 13: Elimination of Imaginaries.

The direction the course should have gone (maybe after Lecture 14/15):

Lecture 15X: Pro-Etale Sheaves.

Lecture 16X-Parametrized Models.

Lecture 17X-Deligne's Theorem; Filtered Colimits.

Lecture 18X-Coverings in Stone_C.

Lecture 19X-Sheaves on Stone_C.

Lecture 21X-Characterizing the image of C.

Lecture 22X-Embedding into Ultrapowers.

Lecture 23X-Compatiblity with Filtered Colimits.

Lecture 24X-Ultracategory Fibrations.

Lecture 28X-Ultrafunctors to Set.

Lecture 30X-Higher Categorical Logic.

Unfinished story, ultimately not needed:

Lecture 14: Locales and Topoi.

Lecture 15: Spaces and Locales.

Lecture 18: Localic Morphisms.

Lecture 19: Reconstruction of Localic Morphisms.

Lecture 20-Locales in a topos.

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