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to the server to view the underlying object.
{
"@context": [
"https://www.w3.org/ns/activitystreams",
{
"ostatus": "http://ostatus.org#",
"atomUri": "ostatus:atomUri",
"inReplyToAtomUri": "ostatus:inReplyToAtomUri",
"conversation": "ostatus:conversation",
"sensitive": "as:sensitive",
"toot": "http://joinmastodon.org/ns#",
"votersCount": "toot:votersCount"
}
],
"id": "https://mathstodon.xyz/users/djspacewhale/statuses/113517317429605692",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/jonmsterling/statuses/113516580997518327",
"published": "2024-11-20T21:06:41Z",
"url": "https://mathstodon.xyz/@djspacewhale/113517317429605692",
"attributedTo": "https://mathstodon.xyz/users/djspacewhale",
"to": [
"https://mathstodon.xyz/users/djspacewhale/followers"
],
"cc": [
"https://www.w3.org/ns/activitystreams#Public",
"https://mathstodon.xyz/users/andrejbauer",
"https://mathstodon.xyz/users/ohad",
"https://mathstodon.xyz/users/MartinEscardo",
"https://mathstodon.xyz/users/jonmsterling"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/djspacewhale/statuses/113517317429605692",
"inReplyToAtomUri": "https://mathstodon.xyz/users/jonmsterling/statuses/113516580997518327",
"conversation": "tag:mathstodon.xyz,2024-11-17:objectId=124197665:objectType=Conversation",
"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@jonmsterling\" class=\"u-url mention\">@<span>jonmsterling</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@MartinEscardo\" class=\"u-url mention\">@<span>MartinEscardo</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@ohad\" class=\"u-url mention\">@<span>ohad</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@andrejbauer\" class=\"u-url mention\">@<span>andrejbauer</span></a></span> ok,,, I still don't know if I'm happy about calling it "cohomology" but do see the utility in having a shorthand for "the 0-truncated hom-space into...". I'd be curious how much of generalized cohomology can be built, as you say, just using representability, though I'm sure that's in their references on the page. On your note about cohomology always being taken "with coefficients in _", is the substantive difference between this language and "evaluation of the functor represented by _" solely in the 0-truncation of the former? or should we, even when spectra à la generalized Eilenberg-MacLane cohomology theories are nowhere in sight, keep deloopings and 'potential' higher cohomology in mind along the way?</p><p>As a postnote on where I'm coming from, I tend to think of a cohomology theory as something represented by a spectrum, the extra algebraic structure induced on each cohomology set and suspension isomorphism and so on being what in my mind separates cohomology theories from the general business of representable functors...</p>",
"contentMap": {
"en": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@jonmsterling\" class=\"u-url mention\">@<span>jonmsterling</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@MartinEscardo\" class=\"u-url mention\">@<span>MartinEscardo</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@ohad\" class=\"u-url mention\">@<span>ohad</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@andrejbauer\" class=\"u-url mention\">@<span>andrejbauer</span></a></span> ok,,, I still don't know if I'm happy about calling it "cohomology" but do see the utility in having a shorthand for "the 0-truncated hom-space into...". I'd be curious how much of generalized cohomology can be built, as you say, just using representability, though I'm sure that's in their references on the page. On your note about cohomology always being taken "with coefficients in _", is the substantive difference between this language and "evaluation of the functor represented by _" solely in the 0-truncation of the former? or should we, even when spectra à la generalized Eilenberg-MacLane cohomology theories are nowhere in sight, keep deloopings and 'potential' higher cohomology in mind along the way?</p><p>As a postnote on where I'm coming from, I tend to think of a cohomology theory as something represented by a spectrum, the extra algebraic structure induced on each cohomology set and suspension isomorphism and so on being what in my mind separates cohomology theories from the general business of representable functors...</p>"
},
"updated": "2024-11-20T21:14:04Z",
"attachment": [],
"tag": [
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/jonmsterling",
"name": "@jonmsterling"
},
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/MartinEscardo",
"name": "@MartinEscardo"
},
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/ohad",
"name": "@ohad"
},
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/andrejbauer",
"name": "@andrejbauer"
}
],
"replies": {
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"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/djspacewhale/statuses/113517317429605692/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/djspacewhale/statuses/113517317429605692/replies",
"items": []
}
},
"likes": {
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},
"shares": {
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}
}