I don't seem to be able to find anything written about Spin TQFT's in dimension (1+1). Does anyone know any references? Or is there some reason it is uninteresting?
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This is covered in Moore and Segal "Dbranes and Ktheory in 2D topological field theory". In particular on around page 16 there is a characterization analogous to "1+1 TQFTs = Commutative Frobenius algebras". 

