A pretty good lecture on *classifying toposes* and their role in mathematics.
Olivia Caramello discusses how toposes came to be studied, how they came to be understood as providing a *semantic core* for a mathematical theory, and how they provide a suitably general context for studying the symmetries (invariants) of a given theory. https://www.youtube.com/watch?v=8xWZpec9pwM -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ |
Did you realize that Lawvere doesn't define the term "topos" until page 352? Frank --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 9, 2020, 10:08 AM Jon Zingale <[hidden email]> wrote: A pretty good lecture on *classifying toposes* and their role in mathematics. - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ |
Ha, yeah. They spend much of the book developing categories that are
simultaneously rich enough to be topos-theoretically interesting and simple enough to reason about their properties/consequences. Recently, another friam member got me thinking about locales[Ɏ], the toy categories presented by Lawvere and Schanuel have been helpful to me in reasoning about them. [Ɏ] From https://ncatlab.org/nlab/show/locale: A locale is, intuitively, like a topological space that may or may not have enough points (or even any points at all). -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ |
Mine's on pg 348. 1997 edition. Mac Lane's is on pg 106 (2nd edition). It would be interesting to know whether the choice(s) were made to introduce the concept earlier later based on the trajectory of the text or the intuitive naturalness of the concept. Oddly, I like the definition Mac Lane gives in the Appendix (pg 289) better than the one on pg 106. But I don't really understand any of it. I've placed Jon's 2 youtube recommendations in The Queue.
On 7/9/20 9:49 AM, Jon Zingale wrote: > Ha, yeah. They spend much of the book developing categories that are > simultaneously rich enough to be topos-theoretically interesting and simple > enough to reason about their properties/consequences. Recently, another > friam member got me thinking about locales[Ɏ], the toy categories presented > by Lawvere and Schanuel have been helpful to me in reasoning about them. > > [Ɏ] From https://ncatlab.org/nlab/show/locale: A locale is, intuitively, > like a topological space that may or may not have enough points (or even any > points at all). On 7/9/20 9:26 AM, Frank Wimberly wrote: > Did you realize that Lawvere doesn't define the term "topos" until page 352? -- ☣ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
uǝʃƃ ⊥ glen
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In reply to this post by jon zingale
Watched a bit of this video.
Sounds like a mathematical description of metaphor -- heh, heh. Nick Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University [hidden email] https://wordpress.clarku.edu/nthompson/ -----Original Message----- From: Friam <[hidden email]> On Behalf Of Jon Zingale Sent: Thursday, July 9, 2020 10:08 AM To: [hidden email] Subject: [FRIAM] Grothendieck toposes and their role in Mathematics A pretty good lecture on *classifying toposes* and their role in mathematics. Olivia Caramello discusses how toposes came to be studied, how they came to be understood as providing a *semantic core* for a mathematical theory, and how they provide a suitably general context for studying the symmetries (invariants) of a given theory. https://www.youtube.com/watch?v=8xWZpec9pwM -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ |
Not just *a* math description of metaphor ... THE math description of metaphor! The Grand Unified Model for metaphor. The more category theory you learn, the closer you'll get to God.
On 7/9/20 11:16 AM, [hidden email] wrote: > Watched a bit of this video. > > Sounds like a mathematical description of metaphor -- heh, heh. -- ☣ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
uǝʃƃ ⊥ glen
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haha, amazing!
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