Notes & Writings

Publications

• Dailey, I., Huggins, C., Mujevic, S. et al. Homotopical Models for Metric Spaces and Completeness. Appl Categor Struct 32, 30 (2024). https://doi.org/10.1007/s10485-024-09788-7 (arXiv)

In progress

• Tensor triangulated categories with sub-Picard grading, work done for the 2023 UChicago Mathematics REU.

Other

• The derived category as an infinity category, a quick set of notes outlining the construction of the derived infinity category of an abelian category, written for a talk I gave at a UCSD Winter 2024 Seminar on higher algebra.
• The standard model structure on spaces, a document written in Winter of 2023 filling in the details of Mark Hovey’s proof of the standard model structure on topological spaces given in his book Model Categories. Warning: the notes are somewhat incomplete, and the proof is given in excruciating detail.
• Category theory slides, slides covering the basics of categories, functors, natural transformations, and (co)limits made for a talk given in a commutative algebra reading group during Summer 2022.