Eric Forgy References

Noncommutative Geometry

• Michel Dubois-violette (pdf), Lectures on Graded Differential Algebras and Noncommutative Geometry

Differential Envelope & Universal Differential Calculus

• R. Coquereaux and D. Kastler, Remarks on the differential envelopes of associative algebras
• H. C. Baehr, A. Dimakis, F. Müller-Hoissen, Differential Calculi on Commutative Algebras
• M. Kontsevich, A. Rosenberg, Noncommutative smooth spaces

Category Theory

• Index (co)limits and (co)ends
• Codescent and the van Kampen Theorem: A lot of good definitions
• Integration (String Coffee Table)
• Metric Spaces, Generalized Logic, and Closed Categories
• Groupoidification Made Easy
• Tales of Groupoification
• Lectures on Integrability of Lie Brackets
• AQFT from Lattice Models
• Noncommutative $\infty$-Lie theory and AQFT (blog)
• Measure on Paths
• “arrow theory”
• Wedge product
• Arrow fields
• Arrow category
• Parity complexes?
• Tangent category, Yoneda, Cayley
• Groupoidification
• Double category (page 6) I’m starting to think that a 2-diamond should somehow be related to a double category. Or maybe even double bicategories
• Lectures on Integrability of Lie Brackets: A very readable introduction to Lie groupoids and Lie algebroids

C* Algebras and Higher Graphs

• C* Algebras of Infinite Graphs
• Graphs, groupoids and Cuntz-Krieger algebras
• Fundamental groupoids of k-graphs
• C* algebras associated to higher-rank graphs