The Categorification of a Symmetric Operad is Independent of Signature

Details The Categorification of a Symmetric Operad is Independent of Signature The Categorification of a Symmetric Operad is Independent of Signature

2007-11-30

arxiv.org/abs/0711.4904v1

Mathematics

Category Theory

Presented at CT2007, June 2007, in Carvoeiro, Portugal

Scientific paper

Given a symmetric operad $P$, and a signature (or generating sequence) $\Phi$ for $P$, we define a notion of the "categorification" (or "weakening") of $P$ with respect to $\Phi$. When $P$ is the symmetric operad whose algebras are commutative monoids, with the standard signature, we recover the notion of symmetric monoidal categories. We then show that this categorification is independent (up to equivalence) of the choice of signature.

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