Timeline for Maps between operads of different arities
Current License: CC BY-SA 3.0
7 events
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| Feb 14, 2013 at 0:06 | comment | added | Vladimir Dotsenko | @Poisson: can you elaborate on this example? What, in your opinion, is not a map of operads? You have written a relation in a particular operad (a quotient of the free operad generated by a unary and a binary operation). Substitution of a binary operation of a unary one is perfectly fine, and produces a binary operation. There is absolutely nothing to be worried about in this particular instance. | |
| Dec 20, 2012 at 18:18 | comment | added | Poisson | Yes, I took another example here, where we map an operation to an operation with more inputs in contrast to the example with fixing inputs where we reduce the number of inputs. Perhaps it was a bit naive to think that a theory existed to take care of these two examples easily. | |
| Dec 20, 2012 at 18:09 | comment | added | Andreas Blass | The specific example in Poisson's comment here doesn't seem to match the original question. | |
| Dec 20, 2012 at 18:05 | comment | added | Poisson | Yes, perhaps I should have been more clear about that. The equation I can express just fine, the problem is that I turn a unary operation into a binary operation, thus it is not a map of operads. | |
| Dec 20, 2012 at 17:56 | comment | added | Tom Leinster | Ah, OK. I was talking about operads of sets, whereas here you probably want operads of vector spaces, also known as linear operads. (Thus, each $P_n$ is a vector space rather than a set.) An equation like the one you mention can be expressed by a linear operad; you don't even need symmetry. | |
| Dec 20, 2012 at 17:42 | comment | added | Poisson | Thanks, I will have a look! The situation I was looking at is the following. Consider the operad of BV-algebras (commutative multiplication m and unary operation d). We can obtain a Gerstenhaber structure by considering [a,b]= d(ab)-d(a)b-ad(b) (ignoring Koszul signs). What does this correspond to at the operad level? | |
| Dec 20, 2012 at 16:56 | history | answered | Tom Leinster | CC BY-SA 3.0 |