Martin Rubey
2007-03-22 15:15:29 UTC
Dear all,
as some of you know, Frederic Chapoton has given a talk on operads at the SLC
in Lyon. I'll just give a (very, very) short account on the connection to
species here. His slides are available online:
http://math.univ-lyon1.fr/~chapoton/
-------------------------------------------------------------------------------
A symmetric operad is a species P together with a morphism
gamma: P o P -> P,
where o is the (usual) composition of (ordinary) species. To add a little
confusion, gamma is also called "composition" or "product"...
gamma can be decomposed into "simple compositions"
o_i : P(I u {i}) x P(J) -> P(I u J)
A non-symmetric operad is the same thing in the world of linear species.
-------------------------------------------------------------------------------
Operads seem to become interesting when one gives them a group structure. But,
in fact, that's my biggest problem with operads: I do not see yet, how I could
use them.
-------------------------------------------------------------------------------
Apart from this, Frederic asked for an implementation of the inverse of the
substitution (of species)... Of course, the result is then a virtual species,
but at least there is a formula in BLL.
And, he confirmed that vectorial species, i.e., functors
(finite) Set -> (finite dimensional) Vector Spaces
would be more interesting...
All the best,
Martin
-------------------------------------------------------------------------
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as some of you know, Frederic Chapoton has given a talk on operads at the SLC
in Lyon. I'll just give a (very, very) short account on the connection to
species here. His slides are available online:
http://math.univ-lyon1.fr/~chapoton/
-------------------------------------------------------------------------------
A symmetric operad is a species P together with a morphism
gamma: P o P -> P,
where o is the (usual) composition of (ordinary) species. To add a little
confusion, gamma is also called "composition" or "product"...
gamma can be decomposed into "simple compositions"
o_i : P(I u {i}) x P(J) -> P(I u J)
A non-symmetric operad is the same thing in the world of linear species.
-------------------------------------------------------------------------------
Operads seem to become interesting when one gives them a group structure. But,
in fact, that's my biggest problem with operads: I do not see yet, how I could
use them.
-------------------------------------------------------------------------------
Apart from this, Frederic asked for an implementation of the inverse of the
substitution (of species)... Of course, the result is then a virtual species,
but at least there is a formula in BLL.
And, he confirmed that vectorial species, i.e., functors
(finite) Set -> (finite dimensional) Vector Spaces
would be more interesting...
All the best,
Martin
-------------------------------------------------------------------------
Take Surveys. Earn Cash. Influence the Future of IT
Join SourceForge.net's Techsay panel and you'll get the chance to share your
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