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"content": "<p>*2024/02/04. Using Yoneda rather than J to present the identity type.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/111874700368118421\" 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/111874700368118421</span></a></p><p>*2024/02/06. The patch of a spectral locale X has fewer points than X.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/111886020216629690\" 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/111886020216629690</span></a></p><p>* 2024/02/16. On Pataraia's fixed-point theorem.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/111943474521669669\" 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/111943474521669669</span></a></p><p>* 2024/02/28. LLPO in constructive mathematics.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112011057976815731\" 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/112011057976815731</span></a></p><p>* 2024/03/07. Teaching program/specification/verification and definition/theorem/proof.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112056560542575049\" 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/112056560542575049</span></a></p><p>*2024/03/14. The subtype of sharp elements of the flat domain of natural numbers.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112096634888563693\" 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/112096634888563693</span></a></p><p>*2024/03/19. Topological intuition for computational, and more generally constructive, mathematics.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112124678815998407\" 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/112124678815998407</span></a></p><p>*2024/04/27. What is a topological space, what is the intuition behind the definition, and what is (roughly) the history of all this.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112344531871296929\" 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/112344531871296929</span></a></p><p>*2024/05/02. Free graphic monoids and the monad of lists without repetitions.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112373111671959398\" 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/112373111671959398</span></a></p><p>*2024/06/14. A question about thinly inhabited types.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112615840084539200\" 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/112615840084539200</span></a></p><p>*2024/06/23. Just for fun, Android/Linux hacking. <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112661718405023763\" 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/112661718405023763</span></a></p><p>*2024/07/18. ¬ WLPO as a weak continuity principle. <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112809256762862829\" 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/112809256762862829</span></a></p><p>*2024/08/21. Continuity of functions ℕ∞ → ℕ.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113001536506411322\" 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/113001536506411322</span></a></p><p>*2024/09/11. When can a function ℕ → ℕ be extended to a function ℕ∞ → ℕ constructively, without assuming continuity axioms? <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113024154634637479\" 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/113024154634637479</span></a></p><p>*2024/09/21. Applying domain theory and topology to come up with seemingly impossible programs.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113177615482791270\" 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/113177615482791270</span></a></p><p>*2024/09/23. Understanding propositional truncations in HoTT/UF. <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113188689591632856\" 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/113188689591632856</span></a></p><p>*2024/12/13. Negative axioms can be postulated without loss of canonicity.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113646659385507211\" 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/113646659385507211</span></a></p><p>3/</p>",
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"en": "<p>*2024/02/04. Using Yoneda rather than J to present the identity type.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/111874700368118421\" 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/111874700368118421</span></a></p><p>*2024/02/06. The patch of a spectral locale X has fewer points than X.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/111886020216629690\" 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/111886020216629690</span></a></p><p>* 2024/02/16. On Pataraia's fixed-point theorem.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/111943474521669669\" 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/111943474521669669</span></a></p><p>* 2024/02/28. LLPO in constructive mathematics.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112011057976815731\" 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/112011057976815731</span></a></p><p>* 2024/03/07. Teaching program/specification/verification and definition/theorem/proof.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112056560542575049\" 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/112056560542575049</span></a></p><p>*2024/03/14. The subtype of sharp elements of the flat domain of natural numbers.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112096634888563693\" 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/112096634888563693</span></a></p><p>*2024/03/19. Topological intuition for computational, and more generally constructive, mathematics.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112124678815998407\" 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/112124678815998407</span></a></p><p>*2024/04/27. What is a topological space, what is the intuition behind the definition, and what is (roughly) the history of all this.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112344531871296929\" 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/112344531871296929</span></a></p><p>*2024/05/02. Free graphic monoids and the monad of lists without repetitions.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112373111671959398\" 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/112373111671959398</span></a></p><p>*2024/06/14. A question about thinly inhabited types.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112615840084539200\" 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/112615840084539200</span></a></p><p>*2024/06/23. Just for fun, Android/Linux hacking. <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112661718405023763\" 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/112661718405023763</span></a></p><p>*2024/07/18. ¬ WLPO as a weak continuity principle. <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/112809256762862829\" 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/112809256762862829</span></a></p><p>*2024/08/21. Continuity of functions ℕ∞ → ℕ.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113001536506411322\" 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/113001536506411322</span></a></p><p>*2024/09/11. When can a function ℕ → ℕ be extended to a function ℕ∞ → ℕ constructively, without assuming continuity axioms? <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113024154634637479\" 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/113024154634637479</span></a></p><p>*2024/09/21. Applying domain theory and topology to come up with seemingly impossible programs.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113177615482791270\" 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/113177615482791270</span></a></p><p>*2024/09/23. Understanding propositional truncations in HoTT/UF. <br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113188689591632856\" 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/113188689591632856</span></a></p><p>*2024/12/13. Negative axioms can be postulated without loss of canonicity.<br /><a href=\"https://mathstodon.xyz/deck/@MartinEscardo/113646659385507211\" 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/113646659385507211</span></a></p><p>3/</p>"
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