Maps (left adjoint arrows) between Frobenius objects in a cartesian bicategory B are precisely comonoid homomorphisms and, for A Frobenius and any T in B, map(B)(T,A) is a groupoid.
Keywords: cartesian bicategory, Frobenius object, dual object, groupoid
2000 MSC: 18A25
Theory and Applications of Categories,
Vol. 20, 2008,
No. 3, pp 25-47.
http://www.tac.mta.ca/tac/volumes/20/3/20-03.dvi
http://www.tac.mta.ca/tac/volumes/20/3/20-03.ps
http://www.tac.mta.ca/tac/volumes/20/3/20-03.pdf
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ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/3/20-03.ps