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Published Online: 12 October 2004
Accepted: June 2004

Frobenius monads and pseudomonoids

Journal of Mathematical Physics 45, 3930 (2004); https://doi.org/10.1063/1.1788852
Ross Street
more...View Affiliations
  • Centre of Australian Category Theory, Macquarie University, New South Wales 2109, Australia
Abstract
Six equivalent definitions of Frobenius algebra in a monoidal category are provided. In a monoidal bicategory, a pseudoalgebra is Frobenius if and only if it is star autonomous. Autonomous pseudoalgebras are also Frobenius. What it means for a morphism of a bicategory to be a projective equivalence is defined; this concept is related to “strongly separable” Frobenius algebras and “weak monoidal Morita equivalence.” Wreath products of Frobenius algebras are discussed.

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