An¬†operad¬†is a gadget used to describe algebraic structures in¬†symmetric monoidal categories. It is a bunch of abstract¬†operations¬†of arbitrarily many arguments, equipped with a notion of how to compose these, subject to evident¬†associativity¬†and¬†unitality¬†conditions. Operads are particularly important and useful in categories with a good notion of homotopy, where they play a key role in organizing hierarchies of higher homotopies.
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Last date updated on September, 2014