Monoidal and Symmetric Categories
Tensor structure, braiding, and applications in physics and topology.
Monoidal and Symmetric Categories. Tensor structure, braiding, and applications in physics and topology.
Foundations and canonical references
The standard treatments of monoidal and symmetric categories approach the subject from complementary angles. Etingof, Tensor Categories (2015) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Lane, Categories for the Working Mathematician (1998) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for monoidal and symmetric categories include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2015Tensor Categoriesetingof-2015, gelaki-2015, nikshych-2015, ostrik-2015
- textbook · primary · 1998Categories for the Working Mathematicianmaclane-1998
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