#category theory | Explore Tumblr Posts and Blogs

janmisali · 3 months

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now if you thought "group" is an unhelpful and nondescriptive name for a mathematical concept. just remember that the broader category of mathematical concepts that groups belong to is called, a "category". so it could always be worse

#jan misali #math #group theory #category theory

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m---a---x · 6 months

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So you people like convoluted diagrams, too?

Here ya go, filthy

#mathblr #set theory #category theory #mathematics

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worlds-smallest-epsilon · 10 months

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One week on HRT and I’ve already bought a category theory textbook 😳

#in my defense it was $30 new #transgender #nonbinary #math #category theory

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abalidoth · 1 year

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hey um. I accidentally hit your boyfriend with a forgetful functor from Boyf to Set and he lost all his algebraic structure. he has the same cardinality but doesn't even have a distinguished element or anything. sorry.

#math stuff #tesserants #category theory

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lipshits-continuous · 3 months

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Considering that I hope to do research in algebraic topology, is learning Category theory worthwhile? I know it'd probably be helpful but I want to know whether the process of trying to learn it would be more beneficial than just learning the relevant stuff as it comes up in the context of algebraic topology

#maths posting #mathblr #maths #mathematics #lipshits posts #topology #algebraic topology #category theory

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art-of-mathematics · 10 months

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I just stumbled upon a magazine (Spektrum der Wissenschaft, Spezial "Abstrakte Welten" (link to a short German version of the article: spektrum.de)) I found in one of my shelves.

Interestingly, I found the picture of "Mathematistan" in there, which I found some years ago somewhere on the internet.

Additionally, there is also a depiction of the "moon of category theory". and I enjoy this analogy.

#math #mathematistan #mathematics #category theory #analogy #analogies #math enjoyment #math enjoyer #mathy

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homotexas · 2 months

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proof by stirring it then blowing a bubble

#nLab moment #category theory #string diagrams

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sailing-the-cylindrical-sea · 1 year

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#math memes #mathematics #category theory

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endofunktor · 9 months

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Hey what is y'all's favorite functor?

Mine's the fundamental group functor going from Top* to Grp.

#mathblr #category theory #asking the void

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bubbloquacious · 8 months

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So if you have a pointed space (X,x), a non-pointed space Y, and a continuous map f: X -> Y, then there is a unique point y in Y such that f is a pointed continuous map (X,x) -> (Y,y) (namely if we take y = f(x)). This phenomenon feels similar to taking a Kleisli extension of a morphism A -> T(B) for some monad T, but among other differences it goes the other direction.

Let U: Topₚ -> Top be the forgetful functor from the category of pointed topological spaces to the category of topological spaces. For every f ∈ Top(U(X),Y) there is a unique Z ∈ Obj(Topₚ) and g ∈ Topₚ(X,Z) such that U(Z) = Y and U(g) = f.

This is used pretty frequently in algebraic topology ('let X,Y be spaces, x ∈ X, and let f: X -> Y be continuous, then f*: π₁(X,x) -> π₁(Y,f(x)), etc.'). I wonder if there's other scenarios that have the same categorical structure?

#math #topology #category theory

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cant-think-of-a-good-one · 9 months

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#haha get it?#CATegory theory #i dont actually fully understand category theory #i think i need to write something long in haskell to fully grasp it #or maybe make my own functional proglang #math #graphs #cats #tabby graphs #yes there will be more

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spectrallysequenced · 4 months

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what is a monad

I know you want me to say that it's a monoid in the category of endofunctors.

Well, that's true, besides the fact that there is no THE category of endofunctors. There is one endofunctor category for any category.

Anyways, that definition is not really helpful. I haven't dealt with monads much (although I have a friend who is kind of obsessed though so i've been ranted at quite a bit). I prefer to think of it defined in terms of adjunctions, because there is a bijective correspondence between adjunctions and monads. One direction is easy, if F,G are an adjoint pair, GF is a monad.

Sadly, I don't feel confident enough to talk about their applications or intuition any further, but I will say that besides being a 2 dollar word for functional programmers who like to pretend to understand category theory, it's a very useful concept in categorical logic. I will say at least the definition is way less opaque than you think, especially when you start unfurling the definitions.

#category theory #math

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m---a---x · 6 months

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Oooooh, i fucking love convoluted, indescipherable diagrams, really gotta show restraint not putting them all over my paper