A small tool to view real-world ActivityPub objects as JSON! Enter a URL
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to the server to view the underlying object.
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"id": "https://mathstodon.xyz/users/joshuagrochow/statuses/113307082296952699",
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"published": "2024-10-14T18:01:08Z",
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"content": "<p>But! TIL there's a categorical definition that supposedly agrees w/ "surjection" on any variety of algebras: </p><p>h is "categorically surjective" (a term I just made up) if for any factorization h=fg with f monic, f must be an iso.</p><p>(h/t Knoebel's book <a href=\"https://doi.org/10.1007/978-0-8176-4642-4\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">doi.org/10.1007/978-0-8176-464</span><span class=\"invisible\">2-4</span></a>) </p><p>Are there categorical definitions that agree w/ injective (resp. surjective) on all concrete categories?</p><p><a href=\"https://mathstodon.xyz/tags/algebra\" class=\"mention hashtag\" rel=\"tag\">#<span>algebra</span></a> <a href=\"https://mathstodon.xyz/tags/CategoryTheory\" class=\"mention hashtag\" rel=\"tag\">#<span>CategoryTheory</span></a> <a href=\"https://mathstodon.xyz/tags/math\" class=\"mention hashtag\" rel=\"tag\">#<span>math</span></a> <a href=\"https://mathstodon.xyz/tags/UniversalAlgebra\" class=\"mention hashtag\" rel=\"tag\">#<span>UniversalAlgebra</span></a></p>",
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"en": "<p>But! TIL there's a categorical definition that supposedly agrees w/ "surjection" on any variety of algebras: </p><p>h is "categorically surjective" (a term I just made up) if for any factorization h=fg with f monic, f must be an iso.</p><p>(h/t Knoebel's book <a href=\"https://doi.org/10.1007/978-0-8176-4642-4\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">doi.org/10.1007/978-0-8176-464</span><span class=\"invisible\">2-4</span></a>) </p><p>Are there categorical definitions that agree w/ injective (resp. surjective) on all concrete categories?</p><p><a href=\"https://mathstodon.xyz/tags/algebra\" class=\"mention hashtag\" rel=\"tag\">#<span>algebra</span></a> <a href=\"https://mathstodon.xyz/tags/CategoryTheory\" class=\"mention hashtag\" rel=\"tag\">#<span>CategoryTheory</span></a> <a href=\"https://mathstodon.xyz/tags/math\" class=\"mention hashtag\" rel=\"tag\">#<span>math</span></a> <a href=\"https://mathstodon.xyz/tags/UniversalAlgebra\" class=\"mention hashtag\" rel=\"tag\">#<span>UniversalAlgebra</span></a></p>"
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