This is unexplained by Arrhenius' definition because we know CO3(2-) acts as a base, but it does not emit an OH- when it reacts, which is what the Arrhenius definition defines as an acid.
The Brönsted-Lowry definition does explain this because CO3(2-) is a proton acceptor, which is what the Brönsted-Lowry definition defines as a base.