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Abstract

These notes offer an introduction to the functorial and algebraic description of two-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.