Notes

Research Lecture Notes

• On the ∞-topos semantics of homotopy type theory, lecture notes to accompany a series of talks delivered at CIRM-Luminy as part of the workshop Logic and Higher Structures.
• ∞-category theory from scratch, from the 2015 Young Topologists’ Meeting.
• Toward the formal theory of (∞,n)-categories, from the 2014 Topologie workshop at Oberwolfach.
• The formal theory of adjunctions, monads, algebras, and descent, from Reimagining the Foundations of Algebraic Topology at MSRI, written by David White.
• Limits of quasi-categories with (co)limits, from Connections for Women: Algebraic Topology at MSRI.
• Made-to-order weak factorization systems, a less-abridged version of an extended conference abstract published by the Centre de Recerca Matemàtica following their Conference on Type Theory, Homotopy Theory, and Univalent Foundations.
• Quasi-categories as (∞,1)-categories, from a talk given in the Thursday Seminar at Harvard.
• Lifting properties and the small object argument, from the Midwest Topology Seminar at Northwestern, written by Gabriel C. Drummond-Cole.

Miscellaneous Mathematical Notes

• Homotopy types as homotopy types, lecture notes from A panorama of homotopy theory: a conference in honour of Mike Hopkins
• Higher category theory, lecture notes from the Thursday Seminar held at Harvard in Spring 2013.
• The algebra and geometry of ∞-categories, written for the Friends of Harvard Mathematics.
• A survey of categorical concepts, written for a graduate topics course.
• On the construction of new topological spaces from existing ones, written for an undergraduate point-set topology class.
• A concise definition of a model category, written for Peter May.
• Homotopy (limits and) colimits, hastily written lecture notes for a talk in the University of Chicago Proseminar.
• Weighted limits and colimits, a slightly expanded version of a talk given by Mike Shulman in 2008.
• Factorization systems, hastily written lecture notes for a talk in the University of Chicago Proseminar.
• A leisurely introduction to simplicial sets, written for fun.