2025-12-28T16:47:30Z https://njump.me Reed Mullanix https://njump.me/npub1ku7w36cvpnnh7vrjk50hwxfhedfeqszs5r0d8gckrdphwvfqjzrssd3a6c https://pool.jortage.com/typespl/accounts/avatars/106/982/880/492/250/214/original/3f37e65d148c2ad5.jpeg https://pool.jortage.com/typespl/accounts/avatars/106/982/880/492/250/214/original/3f37e65d148c2ad5.jpeg https://njump.me/nevent1qqsyqyft0jttxzka3j9udsxdt6r9f3akevcl4gexc4la8haywvpqleczyzmne68tpsxwwlesw2637acexl948yzq2zsda5arzcd5xae3yzggwq3yy96 In reply to <a href='/nevent1qqszkkkgsmnq2u6chjy9mnxq2v4ma7yt0z8kyu8pu92uehzsujuxrkgpzemhxue69uhhyetvv9ujuerfw36x7tnsw43z7ag8fpq'>nevent1q…8fpq</a><br/>_________________________<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzf5l64n2xk9azdrt6c96nwshexx45v4sduj7cyakmw005afuu05jm4rrqe" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzf5l64n2xk9azdrt6c96nwshexx45v4sduj7cyakmw005afuu05jm4rrqe</span> (<span class="italic">nprofile…rrqe</span>)</a></span> Yeah, elaboration on the fly is such a misfeature IMO. This becomes really apparent when you have to do any sort of heavy unification: a problem with bunch of unsolved constraints takes *much* longer to finish than one that has a solution! 2025-12-28T14:57:02Z https://njump.me/nevent1qqs2jnhx2g6eujmpn5swguw7ns7altnwz38l6yrxhhyh8zlfgcqcyagzyzmne68tpsxwwlesw2637acexl948yzq2zsda5arzcd5xae3yzggwzzqhg7 In reply to <a href='/nevent1qqstqk0gtsh7ucjnn20kdchyx9wuskrxczrxy7q6fsvd0rmxgjuqc8spzemhxue69uhhyetvv9ujuerfw36x7tnsw43z7hw3jyr'>nevent1q…3jyr</a><br/>_________________________<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzf5l64n2xk9azdrt6c96nwshexx45v4sduj7cyakmw005afuu05jm4rrqe" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzf5l64n2xk9azdrt6c96nwshexx45v4sduj7cyakmw005afuu05jm4rrqe</span> (<span class="italic">nprofile…rrqe</span>)</a></span> I think you run into trouble here.<br/><br/>What you&#39;ve outlined is equivalent to pulling back Fam(C) along the inclusion `FinSet⁺ → Sets`. If we want the inclusion to preserve the initial object, then the constant family `Const 0 : [1] → C` has to be initial. However, there are two maps `Const 0 → Const 0 + Const 0` 2025-11-17T23:02:37Z https://njump.me/nevent1qqsfm6904lepf3e6mejruqc63y330khkvhm4cu44zcmf4aaqtyv6ftqzyzmne68tpsxwwlesw2637acexl948yzq2zsda5arzcd5xae3yzggwgj5cw6 In reply to <a href='/nevent1qqs8vm2f5szgkyr7vrg337ak0lca03w2dhxnjr5ajhpkznzsumnuxuqpzemhxue69uhhyetvv9ujuerfw36x7tnsw43z7pdcjxn'>nevent1q…cjxn</a><br/>_________________________<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzf5l64n2xk9azdrt6c96nwshexx45v4sduj7cyakmw005afuu05jm4rrqe" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzf5l64n2xk9azdrt6c96nwshexx45v4sduj7cyakmw005afuu05jm4rrqe</span> (<span class="italic">nprofile…rrqe</span>)</a></span> Very much so! The categories I&#39;m looking to complete are the walking parallel arrow categories, so they are directed as well. 2025-11-17T22:21:34Z https://njump.me/nevent1qqsg4x5cjz68arr0cgsnqwk2650wmea2kwk7rud9kzpmtp72eptn6zczyzmne68tpsxwwlesw2637acexl948yzq2zsda5arzcd5xae3yzggwdcu5y6 Is there a clean way of completing a category $C$ with an initial object under *binary* coproducts such that the inclusion of $C$ into the completion preserves the initial object? 2025-11-17T22:15:34Z https://njump.me/nevent1qqs24g8qnrrpylacnqg40cjv96dzhdmtcdrk6fz5yr38dff3ne49qyszyzmne68tpsxwwlesw2637acexl948yzq2zsda5arzcd5xae3yzggwxg5zhs Complexity theory is so cursed because people like to pretend that your model of computation doesn&#39;t matter so long as it&#39;s &#34;reasonable&#34; but like, it does?? 2025-10-08T19:53:21Z https://njump.me/nevent1qqsgc465pzz4jn8lt2s8s0qwtv7mh9g2f96ey7etl87cxrhndgw30mqzyzmne68tpsxwwlesw2637acexl948yzq2zsda5arzcd5xae3yzggw36ahqc It’s sort of funny how HoTT-as-a-metatheory seems completely allergic to any sort of categorical homotopy theory. All the basic notions require your (∞,1) categories to have a _set_ of objects, which always ends up presenting some insurmountable barrier (or forcing you back to square 1 to build a universe of hSets that’s an hSet) 2025-05-03T15:29:25Z