Any plans for a Veeky Forums study group over the summer? What about this?

I'm not that guy but they're saying that in the category set you can identify an element in a set A with a function from a terminal object to A.

Lawere has a first book on CT

lawvere_&_stephen_hoel_schanuel_-_conceptual_mathematics_a_first_introduction_to_categories_[cambridge_university_press_1997_9780521472494]

other famous books:

colin_mclarty_-_elementary_categories_elementary_toposes_[oxford_university_press_1995_9780198514732]

harold_simmons_-_an_introduction_to_category_theory_[cambridge_university_press_2011_9781107010871]

jean-pierre_marquis_-_from_a_geometrical_point_of_view_a_study_of_the_history_and_philosophy_of_category_theory_[springer_2009_9781402093838]
this one is very geometric:
marie_la_palme_reyes_&_gonzalo_reyes_&_houman_zolfaghari_-_generic_figures_and_their_glueings_a_constructive_approach_to_functor_categories_[polimetrica_s.a.s_2004_9788876990045]

>what is subtyping
>implying MLTT is the only type theory to ever exist

>no mac lane
>mfw

...

I'd be game,
although it always happens that I'm the only one who is not "busy with xyz" in the third week, after which people just drop out.

So I take each proposal on Veeky Forums with a grain of salt, you people lack determination and loyalty
:/

>look at me I'm so smart and disciplined xddd

yeha

There is this but it's not just Veeky Forums, rather it's a mix of Veeky Forums, Veeky Forums, and /g/. Possibly Veeky Forums as well.

So far they've covered introductory logic (forallx) and have formed several smaller groups to continue on
>the Open Logic book (typical logic II content)
>Axiomatic Set Theory (Enderton)
>Networking (CCENT Study Guide)
>SICP
>Galois Theory (Ian Stewart)
>Godel Escher Bach

Unfortunately there isn't a category theory group currently running, but if you plan on leading one then you can always propose one. There are a few users versed in category theory already in the group and there has been some interest expressed.

I think the thread to thread model for study groups isn't very robust as it's very difficult to keep users interested in a slow moving thread for that long of a time period. Especially when a retarded gorillaposter is flooding Veeky Forums with obvious bait threads.

still worth it

Wouldn't it be better to start with Int. to Algorithms together with Java and play with stuff practising both at once?

I would not recommend doing this with Haskell tho.

bookzz.org/book/489395/ca1bd6

So when will this start - I'm for soon.

So I was reading into it a little and ended up at the constructible universe, L.

Gödel came up with L and proved it's a model of ZF in which choice holds
(proving consistency of ZFC relative to ZF).

"Def" is also given on that Wikipedia page,
which is used to produce the hierarchy that makes you end up with L:
en.wikipedia.org/wiki/Constructible_universe#What_is_L.3F

Pic related vaguely (for me) describes how the choice for a set A is made.
And then
>One can show that there is a definable well-ordering of L

I wonder, is it somehow related to the fact that you can enumerate the formulas used in the construction of elements of A?

As soon as we can well-order all elements of a set, of course we can just choose the least w.r.t. that order. Anybody know more precisely how this ordering is hone?

I'm interested in the SICP group. I also know Galois theory and can stop by that one.

Please see me mods: [email protected]

bump

I'd like that oxford youtube channel, except I don't know if they upload the slides.
Reminded of it because this was just uploaded

youtube.com/watch?v=yVNZJvOcNHA

what happens in nonassociative geometry

I'd naively assume the analog thing as in non-commutative geometry. The the coordinate functions viewed as operators are chained together not in an associative manner anymore.

Related
mathoverflow.net/questions/133147/what-is-about-nonassociative-geometry

Is there a studygroup for Biology?

I second that notion

I'd love to participate, but they'd have to switch to mattermost instead of slack.

OP here. I might host this. But what platform do you people want?

I'm doing probability/stats, linear dynamical systems, and maybe some control theory

Yah, you well order the formulas. I don't remember how it is done exactly but that's the idea and it shouldn't be hard to formalize.

People seem to like slack, but it might be nice to try something else. Maybe an irc channel or something would be easier to communicate with.

We should just pick out some interesting Papers and do like a Journal Club/Thread

Slack a shit. Please, don't use it. And I'm not saying this only because I'm a /g/entooman.

How about a telegram group?

This, I'm in favor of IRC

I would read on the mclarty article on abuses of topos theory.

a category theorist's category Set is the category of sets and set functions, but this is not the same a set theorists von neumann universe, for example, which doesn't even form a category.

So basically, there ISN'T a good set notion of "category of sets", at least not one that will bring you richer information at the function-theoretic level than the categorical definition.

However, once you forget about the cumulative hierarchy, which is rarely used in any applications of sets anyway outside of constructions of ordinals, cardinals, etc., you get a category of objects called "sets" which have "elements" which you only care about insofar as the elements of A are distinct from each other (i.e. you know when a≠b in A, but you cannot compare elements of A and B without providing a morphism between them). At this level, the topos/categorical formulation works (with much less axiomatization than set theory), but you are right that there is no notion of "element" in this kind of set theory. In fact, category theory cannot even encode such a relation; rather, elementhood is defined from functions categorically, not the other way around; effectively "elements" are just singleton subsets, and there is a way to state "singleton" topos theoretically without making reference to elements. but there is no notion of cumulative hierarchy without just building it as a formal object itself within some category.

I should clarify; a cumulative hierarchy style class of sets can be used as the objects of a category, by looking at set-functions between them as the morphisms, but at that point the category has "forgotten" about the cumulative hierarchy anyway at the level of morphisms (a set function doesn't care about elements of elements). You can use set theory to determine whether two sets are equal or not, but generally equality is not what you care about in category theory, but rather isomorphism. At that point, you have "forgotten" the explicit contents of each set, and you are back to the category theorist's notion.

I'd like Mattermost, it's like slack but free and open source and self hosted.

vuu

but IRC channels you must run all the time to no lose track of what people said, no?

Besides, doing it anywhere besides in Veeky Forums threads makes the chance of people staying interested even small than it already is.
Just make regular threads for anyone to see, even lurkers who don't sign up. It's your only hope.

So I started playing with Idris and implementing some basics. It's fun!

P in pic related maps a pair of functions
[math] f\in Z^X [/math] and [math] g\in Z^Y [/math]
to the set
[math] \{ (t_x, t_y)\in X \times Y \ | \ f(t_x)=g(t_y) \} [/math]

a.k.a. the solution set of [math] f(t_x)=g(t_y) [/math],
a.k.a. a filtered version of the Cartesian product,
a.k.a. the object [math] X\times_Z Y[/math],
a.k.a. the pullback of [math] f [/math] along [math] g [/math] in a category of sets.

E.g. it maps [math] f(k)=8k [/math] and [math] g(n)=n^2 [/math] to the set
[math] \{ (k, n) \ | \ 8k=n^2 \} [/math]

muh type knows the full specification of the objects

>tfw can't write homotopy equivalences to produce proofs of equality

I'd like to, but to complicated for me. I'm still doing elementary algebra. Be sure to store/post online for reference for future use. I'd love to read/hear/see what you've done.

It's not actually harder than elementary algebra,
just less about numbers and thus less easy applicable to physics and engineering problems.

bnup?

I would also be interested in this. Currently going through Naive Set Theory by Halmos. Planning on starting:
Baby Rudin
Mendelson's Introduction to Topology
Tolstov's Fourier Series

As for the platform, IRC would work for me. Anything works though

>random math text book with lots of interesting advance math/proofs/puzzles
Name pls?

The book Conceptual Mathematics is so slow going, I wonder if that's necessary even for absolute beginners.

That's literally true.