En-ring

In mathematics, an -algebra in a C consists of the following data: An for any open subset U of Rn homeomorphic to an n-disk. 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 n-disks operad. 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. An -algebra in is a if n = 1, a if n = 2, and a if n ≥ 3. If Λ is a commutative ring, then defines an -algebra in the infinity category of chain complexes of -modules.