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Lecture notes on 2-dimensional defect TQFT
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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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Cited by 2 Pith papers
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Formal Languages and TQFTs with Defects
A Boolean 1D TQFT-with-defects construction for regular languages is shown to be functorial under transducers and generalized to context-free grammars via an operadic Chomsky-Schützenberger theorem.
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Topological defects in reflection positive topological field theories
A reflection-positive two-dimensional defect TQFT gives its defect bicategory an O(2)-dagger structure, and with positivity a structure close to a 3-Hilbert space.
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