  This paper presents the structure conversion by which from an Ann-category
$\A,$ we can obtain its reduced Ann-category of the type $(R,M)$ whose
structure is a family of five functions $k=(\xi,\eta,\alpha,\lambda,\rho)$.
Then we will show that each Ann-category is determined by three invariants:
  1. The ring $\Pi_0(\A)$ of the isomorphic classes of objects of $\A$,
  2. $\Pi_0(\A)$-bimodule $\Pi_1(\A) = \Aut_{\A}(0),$
  3. The element $ \bar{k}\in H^{3}_{M}(\Pi_0(\A), \Pi_1(\A))$ (the ring
cohomology due to MacLane).
