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# En-ring

In mathematics, an ${\displaystyle {\mathcal {E}}_{n}}$-algebra in a symmetric monoidal infinity category C consists of the following data:

• An object ${\displaystyle A(U)}$ for any open subset U of Rn homeomorphic to an n-disk.
• A multiplication map:
${\displaystyle \mu :A(U_{1})\otimes \cdots \otimes A(U_{m})\to A(V)}$
for any disjoint open disks ${\displaystyle U_{j}}$ contained in some open disk V

subject to the requirements that the multiplication maps are compatible with composition, and that ${\displaystyle \mu }$ is an equivalence if ${\displaystyle m=1}$. An equivalent definition is that A is an algebra in C over the little n-disks operad.