# Category:Definitions/Subset Products

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This category contains definitions related to Subset Products.

Related results can be found in Category:Subset Products.

Let $\struct {S, \circ}$ be an algebraic structure.

We can define an operation on the power set $\powerset S$ as follows:

- $\forall A, B \in \powerset S: A \circ_\mathcal P B = \set {a \circ b: a \in A, b \in B}$

This is called the **operation induced on $\powerset S$ by $\circ$**, and $A \circ_\mathcal P B$ is called the **subset product** of $A$ and $B$.

## Subcategories

This category has only the following subcategory.