2026-07-06T13:57:21Z https://nostr.now Bruno Gavranović https://nostr.now/npub1as5wuenwxtp52fgk2u6km8drqg70zwras7hr0g9gfqp6ffmajdzqfzm3d3 https://media.mathstodon.xyz/accounts/avatars/109/536/193/392/190/234/original/bef7c76943d895ad.jpg https://media.mathstodon.xyz/accounts/avatars/109/536/193/392/190/234/original/bef7c76943d895ad.jpg https://nostr.now/nevent1qqsgpt4j9975aksjl3luj4c947w84u9ntte0ms3ta7f4sfjae8g5dtczyrkz3mnxdcevx3f9zetn2mva5vpreufc0kr6udaq4pyq8f980kf5gzqxg9r In reply to <a href='/nevent1qqsv5tt9m9e2mqn2casml66k86acyxegww6tj5ynq0j8ghgzcu9nc5gpz4mhxue69uhhyetvv9ujuerfw36x7tnsw43qsjeztw'>nevent1q…eztw</a><br/>_________________________<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqky223zcc4q69d8t0me4vg5uw8mw0yxeukjgvz6h92laqnenr0ajs7297ud" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqky223zcc4q69d8t0me4vg5uw8mw0yxeukjgvz6h92laqnenr0ajs7297ud</span> (<span class="italic">nprofile…97ud</span>)</a></span> I think there is some care that needs to be taken when upgrading the &#34;removing element of a set&#34; story to &#34;removing an object of a category&#34; one.<br/><br/>For instance, if there was another object `q` isomorphic to `p0` we removed, we&#39;d end up with an equivalent category. So you likely want to remove the entire isomorphism class, but then I believe you run into further problems. <br/><br/>This thesis on Symmetric Containers (Section 2.3) goes into some detail: <a href="https://staff.math.su.se/gylterud/thesis_gylterud.pdf">https://staff.math.su.se/gylterud/thesis_gylterud.pdf</a> 2026-01-27T16:30:15Z https://nostr.now/nevent1qqs2u37vel4w00dqs7r8qgn6f9q2s3v38z2uzpyhtatxk8zjn4rt9aqzyrkz3mnxdcevx3f9zetn2mva5vpreufc0kr6udaq4pyq8f980kf5gke577g In reply to <a href='/nevent1qqsftdu6c3n4wg3j7prcs37458wg3g28qa9008av7pafj99rjzqjdugpzemhxue69uhhyetvv9ujuerfw36x7tnsw43z7qgglha'>nevent1q…glha</a><br/>_________________________<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyr2u6559vtv0nfk2m0995f4vcahyyktsy42ay7zdztq6e2uklmwqjwwp3nn" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyr2u6559vtv0nfk2m0995f4vcahyyktsy42ay7zdztq6e2uklmwqjwwp3nn</span> (<span class="italic">nprofile…p3nn</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzc3f2ytrz5rg45adl0x43zn3cldeusm8j6fpst2u4tl5z0xvdlk2rj4x5t" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzc3f2ytrz5rg45adl0x43zn3cldeusm8j6fpst2u4tl5z0xvdlk2rj4x5t</span> (<span class="italic">nprofile…4x5t</span>)</a></span> It did - the Appendix B of my thesis contains an intro and relevant constuctions of locally graded (and indexed) categories, and unpacks how one obtains Para as a change of base along the category of elements<br/><br/><a href="https://arxiv.org/abs/2403.13001">https://arxiv.org/abs/2403.13001</a> 2025-11-10T12:11:44Z