TL;DR
This paper introduces a functorial and algebraic framework for 2D defect topological quantum field theories, extending the relation to Frobenius algebras to pivotal 2-categories, with applications to open/closed TQFTs and Calabi-Yau categories.
Contribution
It generalizes the algebraic description of 2D TQFTs with defects to pivotal 2-categories and details their relation to open/closed TQFTs and Calabi-Yau categories.
Findings
Construction of pivotal 2-categories from defect TQFTs
Equivalence of open/closed TQFTs to Calabi-Yau categories
Extraction of algebraic data from pivotal 2-categories
Abstract
These notes offer an introduction to the functorial and algebraic description of 2-dimensional topological quantum field theories `with defects', assuming only superficial familiarity with closed TQFTs in terms of commutative Frobenius algebras. The generalisation of this relation is a construction of pivotal 2-categories from defect TQFTs. We review this construction in detail, flanked by a range of examples. Furthermore we explain how open/closed TQFTs are equivalent to Calabi-Yau categories and the Cardy condition, and how to extract such data from pivotal 2-categories.
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