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Fusion category
In
mathematics
, a
fusion
category
is a category that is
rigid
,
semisimple
,
-linear
,
monoidal
and has only
finitely many
isomorphism
classes
of
simple objects
, such that the monoidal
unit
is
simple
. If the
ground field
is
algebraically closed
, then the
latter
is
equivalent
to by
Schur's lemma
.
Examples
Representation Category of a finite group
Reconstruction
Under
Tannaka-Krein duality
, every fusion category arises as the
representations
of a
weak Hopf algebra
.