tag:dreamwidth.org,2016-12-25:2614584timeletstimeletstimelets2025-02-03T07:31:21Ztag:dreamwidth.org,2016-12-25:2614584:1615058timelets @ 2025-02-02T23:18:002025-02-03T07:31:21Z2025-02-03T07:31:21Zpublic0I keep coming back to this video about the relationship between (pre-)sheafs and cohomology. Here he says that "the number one technique in mathematics is turning any problem into a linear algebra problem.<br /><br />More generally, Lawvere often talks about mapping geometry to algebra. <br /><br /><a href="https://youtu.be/RPuWHN0BTio?si=U0h7YM-3GlcyvnS5&t=1890">https://youtu.be/RPuWHN0BTio?si=U0h7YM-3GlcyvnS5&t=1890</a><br /><br /><img src="https://timelets.dreamwidth.org/file/350641.png" /><br /><br />D --> J <-- T ( c: D --> T is the solution to a choice problem, per Lawvere). <br /><br />d: D --> J<br />e: T --> J<br />c: D --> T<br /><br />This diagram is a regular Kan extension problem, with a cohomology twist, i.e. assigning values to both objects and arrows.<br /><br /><img src="https://www.dreamwidth.org/tools/commentcount?user=timelets&ditemid=1615058" width="30" height="12" alt="comment count unavailable" style="vertical-align: middle;"/> comments