A large circular operator symbol commonly used for direct products or tensor products in algebra and category theory.
Examples
Direct product of vector spaces
V = \bigodot_{i=1}^n V_i
Cyclic product operation in group theory
G = \bigodot_{k=1}^m G_k \text{ where } G_k \cong \mathbb{Z}_2
Tensor product of multiple spaces
\mathcal{H} = \bigodot_{j=1}^N \mathcal{H}_j