  The relation between crossed product and $H$-Galois extension in braided
tensor category ${\cal C}$ with equivalisers and coequivalisers is established.
That is, it is shown that if there exist an equivaliser and a coequivaliser for
any two morphisms in ${\cal C}$, then $A = B #_\sigma H$ is a crossed product
algebra if and only if the extension $A/B$ is Galois, the canonical epic $q:
A\otimes A \to A\otimes_B A$ is split and $A$ is isomorphic as left $B$-modules
and right $H$-comodules to $B\otimes H$ in ${\cal C}$.
