Research Paper#Topological Quantum Field Theory, Category Theory🔬 ResearchAnalyzed: Jan 3, 2026 17:05
Coherent 2D TQFTs via Spans and 2-Segal Sets
Analysis
This paper explores the mathematical structure of 2-dimensional topological quantum field theories (TQFTs). It establishes a connection between commutative Frobenius pseudomonoids in the bicategory of spans and 2-Segal cosymmetric sets. This provides a new perspective on constructing and understanding these TQFTs, potentially leading to advancements in related fields like quantum computation and string theory. The construction from partial monoids is also significant, offering a method for generating these structures.
Key Takeaways
- •Establishes a correspondence between algebraic structures (Frobenius pseudomonoids) and geometric structures (2-Segal cosymmetric sets) in the context of 2D TQFTs.
- •Provides a new way to construct and analyze 2D TQFTs.
- •Offers a method for generating 2-Segal cosymmetric sets from partial monoids.
Reference
“The paper shows that commutative Frobenius pseudomonoids in the bicategory of spans are in correspondence with 2-Segal cosymmetric sets.”