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"content": "<p>* 2025/04/12. A universal characterization of the closed Euclidean interval.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114325340007735876\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114325340007735876</span></a></p><p>*2025/05/14. Computing all optimal plays of a sequential game.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114506199078361520\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114506199078361520</span></a></p><p>*2025/05/20. Internal effectful forcing.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114541967632998444\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114541967632998444</span></a></p><p>*2025/05/21. A positive way of saying that a type is different from the unit type, in connection with the lifting monad.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114547664640960020\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114547664640960020</span></a></p><p>*2025/06/05. Taking "algebraically" seriously in the definition of algebraically injective type.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114633174055141602\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114633174055141602</span></a></p><p>*2025/06/20. The fundamental lemma of transport along equivalences.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114717657709706036\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114717657709706036</span></a></p><p>*2025/06/22. Question about object classifiers and univalence.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114722727504214914\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114722727504214914</span></a></p><p>*2025/06/26. Dependent equality in dependent type theory.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114751426538568913\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114751426538568913</span></a></p><p>*2025/07/01. A proof that the type of natural numbers is a set in MLTT without universes by Evan Cavallo. <br /><a href=\"https://mathstodon.xyz/deck/@ncf@types.pl/114779291804001070\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@ncf@types</span><span class=\"invisible\">.pl/114779291804001070</span></a></p><p>The above is a thread started by <span class=\"h-card\" translate=\"no\"><a href=\"https://types.pl/@ncf\" class=\"u-url mention\">@<span>ncf</span></a></span> with that question, and eventually answered by <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@ecavallo\" class=\"u-url mention\">@<span>ecavallo</span></a></span> . I made wrong statements in that thread, but I am keeping them without correction (people corrected me there).</p><p>4/</p>",
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"en": "<p>* 2025/04/12. A universal characterization of the closed Euclidean interval.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114325340007735876\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114325340007735876</span></a></p><p>*2025/05/14. Computing all optimal plays of a sequential game.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114506199078361520\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114506199078361520</span></a></p><p>*2025/05/20. Internal effectful forcing.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114541967632998444\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114541967632998444</span></a></p><p>*2025/05/21. A positive way of saying that a type is different from the unit type, in connection with the lifting monad.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114547664640960020\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114547664640960020</span></a></p><p>*2025/06/05. Taking "algebraically" seriously in the definition of algebraically injective type.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114633174055141602\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114633174055141602</span></a></p><p>*2025/06/20. The fundamental lemma of transport along equivalences.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114717657709706036\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114717657709706036</span></a></p><p>*2025/06/22. Question about object classifiers and univalence.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114722727504214914\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114722727504214914</span></a></p><p>*2025/06/26. Dependent equality in dependent type theory.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/114751426538568913\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@MartinEsc</span><span class=\"invisible\">ardo/114751426538568913</span></a></p><p>*2025/07/01. A proof that the type of natural numbers is a set in MLTT without universes by Evan Cavallo. <br /><a href=\"https://mathstodon.xyz/deck/@ncf@types.pl/114779291804001070\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">mathstodon.xyz/deck/@ncf@types</span><span class=\"invisible\">.pl/114779291804001070</span></a></p><p>The above is a thread started by <span class=\"h-card\" translate=\"no\"><a href=\"https://types.pl/@ncf\" class=\"u-url mention\">@<span>ncf</span></a></span> with that question, and eventually answered by <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@ecavallo\" class=\"u-url mention\">@<span>ecavallo</span></a></span> . I made wrong statements in that thread, but I am keeping them without correction (people corrected me there).</p><p>4/</p>"
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