In mathematics, an algebra in a symmetric monoidal infinity category C consists of the following data:
 An object for any open subset U of R^{n} homeomorphic to an ndisk.
 A multiplication map:
 for any disjoint open disks contained in some open disk V
subject to the requirements that the multiplication maps are compatible with composition, and that is an equivalence if . An equivalent definition is that A is an algebra in C over the little ndisks operad.
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Transcription
Examples
 An algebra in vector spaces over a field is a unital associative algebra if n = 1, and a unital commutative associative algebra if n ≥ 2.^{[citation needed]}
 An algebra in categories is a monoidal category if n = 1, a braided monoidal category if n = 2, and a symmetric monoidal category if n ≥ 3.
 If Λ is a commutative ring, then defines an algebra in the infinity category of chain complexes of modules.
See also
References
 http://www.math.harvard.edu/~lurie/282ynotes/LectureXXIIEn.pdf
 http://www.math.harvard.edu/~lurie/282ynotes/LectureXXIIIKoszul.pdf
External links