Frobenius monoidal functor
With duals for objects
With duals for morphisms
Special sorts of products
In higher category theory
A functor between monoidal categories which is both a lax monoidal functor and an oplax monoidal functor is called Frobenius if the structure morphisms for the lax monoidal structure
and for the oplax monoidal structure
satisfy the axioms of a Frobenius algebra in that (in string diagram notation) for all objects in we have
The Moore complex functor
from abeliam simplicial groups to connective chain complexes is Frobenius, as is the normalzed chains complex functor
For more on this see monoidal Dold-Kan correspondence.
Equation (3.26), (3.27) in p. 81 of
- M. B. McCurdy, R. Street, What separable Frobenius monoidal functors preserve, arxiv/0904.3449 and Cahiers TGDC, 51 (2010)p. 29 - 50.
Revised on April 13, 2011 18:21:28
by Tim Porter