Is it possible to “mod” the action of a symmetric group on a symmetric operad? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Order of a set $X$ acted upon transitively by the Symmetric GroupTriviality of the principal fiber bundle obtained from quotienting a manifold by a free and proper actionExistence of slices for the action of a subgroupSpaces homotopy equivalent to $A_infty$-spacesClarification of notion of proper group action.What is a group action, and how can we apply it to Sylow theoryGroup action of Symmetric group on arbitrary set AThe Modules over Algebras over Operads are not what they seem.Action of a symmetric group in operadBase change of topological operad to any symmetric monoidal model category and $E_n$-algebras outside of $textbfTop$
Can a non-EU citizen traveling with me come with me through the EU passport line?
Stars Make Stars
Right-skewed distribution with mean equals to mode?
Is there a "higher Segal conjecture"?
What is the longest distance a 13th-level monk can jump while attacking on the same turn?
Models of set theory where not every set can be linearly ordered
Storing hydrofluoric acid before the invention of plastics
What does the "x" in "x86" represent?
Is a manifold-with-boundary with given interior and non-empty boundary essentially unique?
How can players work together to take actions that are otherwise impossible?
Gastric acid as a weapon
Why did the IBM 650 use bi-quinary?
What are the motives behind Cersei's orders given to Bronn?
Is there a documented rationale why the House Ways and Means chairman can demand tax info?
Proof involving the spectral radius and the Jordan canonical form
What's the difference between `auto x = vector<int>()` and `vector<int> x`?
How to recreate this effect in Photoshop?
Single word antonym of "flightless"
What do you call a phrase that's not an idiom yet?
What is the correct way to use the pinch test for dehydration?
What LEGO pieces have "real-world" functionality?
Withdrew £2800, but only £2000 shows as withdrawn on online banking; what are my obligations?
How to find all the available tools in macOS terminal?
Is it true that "carbohydrates are of no use for the basal metabolic need"?
Is it possible to “mod” the action of a symmetric group on a symmetric operad?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Order of a set $X$ acted upon transitively by the Symmetric GroupTriviality of the principal fiber bundle obtained from quotienting a manifold by a free and proper actionExistence of slices for the action of a subgroupSpaces homotopy equivalent to $A_infty$-spacesClarification of notion of proper group action.What is a group action, and how can we apply it to Sylow theoryGroup action of Symmetric group on arbitrary set AThe Modules over Algebras over Operads are not what they seem.Action of a symmetric group in operadBase change of topological operad to any symmetric monoidal model category and $E_n$-algebras outside of $textbfTop$
$begingroup$
I am relatively new to category theory, so only have a rough understanding of the technicalities behind operads. My understanding is that symmetric operads are defined so that they are "nicely" acted on by the symmetric group.
My question is: Is it possible to alter this action i.e. quotient the action so that a proper subgroup of the symmetric group acts on the operad?
I do not see how this would raise any issues with the definition of the symmetric operad (for example I think you still have equivariance), but am wondering if any technicalities would prevent me from doing this.
group-theory category-theory symmetric-groups group-actions operads
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
$endgroup$
add a comment |
$begingroup$
I am relatively new to category theory, so only have a rough understanding of the technicalities behind operads. My understanding is that symmetric operads are defined so that they are "nicely" acted on by the symmetric group.
My question is: Is it possible to alter this action i.e. quotient the action so that a proper subgroup of the symmetric group acts on the operad?
I do not see how this would raise any issues with the definition of the symmetric operad (for example I think you still have equivariance), but am wondering if any technicalities would prevent me from doing this.
group-theory category-theory symmetric-groups group-actions operads
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
$endgroup$
2
$begingroup$
For full disclosure, I know nothing about operads. But in all the applications I know of, if a group acts on something, so does any of its proper subgroups, and you don't need to take a quotient to realize this action, it's just a restriction.
$endgroup$
– Matt Samuel
Mar 25 at 22:36
$begingroup$
I don't understand the question. An operad consists of various bits which have various symmetric group actions on them. You can certainly take a particular operad and restrict these actions to subgroups. But it sounds like what you want is to alter the definition, to make a new type of operad involving actions by various subgroups of the symmetric groups. Is that right?
$endgroup$
– Qiaochu Yuan
Mar 25 at 23:48
$begingroup$
Yes, that's exactly what I mean. I'm wondering if I can define a new type of operad by somehow altering the action of the symmetric group on a symmetric operad.
$endgroup$
– Brendan Mallery
Mar 26 at 0:25
add a comment |
$begingroup$
I am relatively new to category theory, so only have a rough understanding of the technicalities behind operads. My understanding is that symmetric operads are defined so that they are "nicely" acted on by the symmetric group.
My question is: Is it possible to alter this action i.e. quotient the action so that a proper subgroup of the symmetric group acts on the operad?
I do not see how this would raise any issues with the definition of the symmetric operad (for example I think you still have equivariance), but am wondering if any technicalities would prevent me from doing this.
group-theory category-theory symmetric-groups group-actions operads
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
$endgroup$
I am relatively new to category theory, so only have a rough understanding of the technicalities behind operads. My understanding is that symmetric operads are defined so that they are "nicely" acted on by the symmetric group.
My question is: Is it possible to alter this action i.e. quotient the action so that a proper subgroup of the symmetric group acts on the operad?
I do not see how this would raise any issues with the definition of the symmetric operad (for example I think you still have equivariance), but am wondering if any technicalities would prevent me from doing this.
group-theory category-theory symmetric-groups group-actions operads
group-theory category-theory symmetric-groups group-actions operads
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
asked Mar 25 at 22:33
Brendan MalleryBrendan Mallery
61
61
2
$begingroup$
For full disclosure, I know nothing about operads. But in all the applications I know of, if a group acts on something, so does any of its proper subgroups, and you don't need to take a quotient to realize this action, it's just a restriction.
$endgroup$
– Matt Samuel
Mar 25 at 22:36
$begingroup$
I don't understand the question. An operad consists of various bits which have various symmetric group actions on them. You can certainly take a particular operad and restrict these actions to subgroups. But it sounds like what you want is to alter the definition, to make a new type of operad involving actions by various subgroups of the symmetric groups. Is that right?
$endgroup$
– Qiaochu Yuan
Mar 25 at 23:48
$begingroup$
Yes, that's exactly what I mean. I'm wondering if I can define a new type of operad by somehow altering the action of the symmetric group on a symmetric operad.
$endgroup$
– Brendan Mallery
Mar 26 at 0:25
add a comment |
2
$begingroup$
For full disclosure, I know nothing about operads. But in all the applications I know of, if a group acts on something, so does any of its proper subgroups, and you don't need to take a quotient to realize this action, it's just a restriction.
$endgroup$
– Matt Samuel
Mar 25 at 22:36
$begingroup$
I don't understand the question. An operad consists of various bits which have various symmetric group actions on them. You can certainly take a particular operad and restrict these actions to subgroups. But it sounds like what you want is to alter the definition, to make a new type of operad involving actions by various subgroups of the symmetric groups. Is that right?
$endgroup$
– Qiaochu Yuan
Mar 25 at 23:48
$begingroup$
Yes, that's exactly what I mean. I'm wondering if I can define a new type of operad by somehow altering the action of the symmetric group on a symmetric operad.
$endgroup$
– Brendan Mallery
Mar 26 at 0:25
2
2
$begingroup$
For full disclosure, I know nothing about operads. But in all the applications I know of, if a group acts on something, so does any of its proper subgroups, and you don't need to take a quotient to realize this action, it's just a restriction.
$endgroup$
– Matt Samuel
Mar 25 at 22:36
$begingroup$
For full disclosure, I know nothing about operads. But in all the applications I know of, if a group acts on something, so does any of its proper subgroups, and you don't need to take a quotient to realize this action, it's just a restriction.
$endgroup$
– Matt Samuel
Mar 25 at 22:36
$begingroup$
I don't understand the question. An operad consists of various bits which have various symmetric group actions on them. You can certainly take a particular operad and restrict these actions to subgroups. But it sounds like what you want is to alter the definition, to make a new type of operad involving actions by various subgroups of the symmetric groups. Is that right?
$endgroup$
– Qiaochu Yuan
Mar 25 at 23:48
$begingroup$
I don't understand the question. An operad consists of various bits which have various symmetric group actions on them. You can certainly take a particular operad and restrict these actions to subgroups. But it sounds like what you want is to alter the definition, to make a new type of operad involving actions by various subgroups of the symmetric groups. Is that right?
$endgroup$
– Qiaochu Yuan
Mar 25 at 23:48
$begingroup$
Yes, that's exactly what I mean. I'm wondering if I can define a new type of operad by somehow altering the action of the symmetric group on a symmetric operad.
$endgroup$
– Brendan Mallery
Mar 26 at 0:25
$begingroup$
Yes, that's exactly what I mean. I'm wondering if I can define a new type of operad by somehow altering the action of the symmetric group on a symmetric operad.
$endgroup$
– Brendan Mallery
Mar 26 at 0:25
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Yes. (This paper formulates extra structure on a sequence $G_0,G_1,dots$ of groups to get a theory analogous to the theory of operads.)
answered Apr 1 at 1:29
tcampstcamps
3,2191022
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3162416%2fis-it-possible-to-mod-the-action-of-a-symmetric-group-on-a-symmetric-operad%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes. (This paper formulates extra structure on a sequence $G_0,G_1,dots$ of groups to get a theory analogous to the theory of operads.)
answered Apr 1 at 1:29
tcampstcamps
3,2191022
$endgroup$
add a comment |
$begingroup$
Yes. (This paper formulates extra structure on a sequence $G_0,G_1,dots$ of groups to get a theory analogous to the theory of operads.)
answered Apr 1 at 1:29
tcampstcamps
3,2191022
$endgroup$
add a comment |
$begingroup$
Yes. (This paper formulates extra structure on a sequence $G_0,G_1,dots$ of groups to get a theory analogous to the theory of operads.)
answered Apr 1 at 1:29
tcampstcamps
3,2191022
$endgroup$
Yes. (This paper formulates extra structure on a sequence $G_0,G_1,dots$ of groups to get a theory analogous to the theory of operads.)
answered Apr 1 at 1:29
tcampstcamps
3,2191022
answered Apr 1 at 1:29
tcampstcamps
3,2191022
answered Apr 1 at 1:29
tcampstcamps
3,2191022
answered Apr 1 at 1:29
tcampstcamps
3,2191022
3,2191022
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3162416%2fis-it-possible-to-mod-the-action-of-a-symmetric-group-on-a-symmetric-operad%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
For full disclosure, I know nothing about operads. But in all the applications I know of, if a group acts on something, so does any of its proper subgroups, and you don't need to take a quotient to realize this action, it's just a restriction.
$endgroup$
– Matt Samuel
Mar 25 at 22:36
$begingroup$
I don't understand the question. An operad consists of various bits which have various symmetric group actions on them. You can certainly take a particular operad and restrict these actions to subgroups. But it sounds like what you want is to alter the definition, to make a new type of operad involving actions by various subgroups of the symmetric groups. Is that right?
$endgroup$
– Qiaochu Yuan
Mar 25 at 23:48
$begingroup$
Yes, that's exactly what I mean. I'm wondering if I can define a new type of operad by somehow altering the action of the symmetric group on a symmetric operad.
$endgroup$
– Brendan Mallery
Mar 26 at 0:25