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Category Theory is like Set Theory, but supposedly better. What is it, though?

  • It’s a collection of points, and arrows.
  • Unlike in Set Theory, things can’t just be there, without a meaning attached.
  • No wonder they call it “abstract nonsense"…

An example, then. Maybe you noticed…

Set Theory, Category Theory, and philosophy. Interesting

Tags: ilovemath
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isomorphismes:

Commutativity is an easy property to render into English: it means order doesn’t matter.

http://2.bp.blogspot.com/-kqL0IAUkfQE/Tb8ik3KuGHI/AAAAAAAAAGc/1iHHkGauUfQ/s1600/rubiks+layout+001.jpg

Watchmen

For example “three groups of five rocks” totals the same as “five groups of three rocks”. In fact a general proposition is true: “L groups of R rocks” totals the same as “R groups of L…

Interesting. I’m not sure how I never realized that exponents weren’t associative. My go-to example was always subtraction.

(2^2)^2 = 2^(2^2) holds; both equal 16. But 16^2 is not the same as 2^16. If I’d carried it one step further in my thoughts, I might have realized the non-associativity of exponentiation :)

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A sudoku of linear functionals

isomorphismes:

Today’s glossary provoked by Michael Spivak.

tensors spivak diff geom vol 1 ch 4

Below I’ve drawn two vector spaces connected by a linear homomorphism ƒ, plus a linear functional λ going to ℝ. After seeing these pictures I hope it’s easier to understand how the pullback ƒ* works.

Here’s one of the main pictures for flavour:

dual space linear functional

Also, you can probably just skim the pictures and get the point (especially the Number Field one and the final one). That’s the fastest way to read this post.



Start with an abstract 𝓥ector space.

abstract vector space

I’ll do some violence because I’ll need coordinates in a minute.

invent linear functional

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brazilwonders:

Rapadura 

#yoloquiero

brazilwonders:

Rapadura 

#yoloquiero

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"No tengo sueños asi que no sé si estoy dormido."

— Cevladé.- El vaso medio roto (via entrehumoyalcoholx)

(via esta-night-no)

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a minha tem 3 anos de história kkkk

a minha tem 3 anos de história kkkk

(via esta-night-no)

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Life as I know it turned 3 today!

I’ve been tumbling for three years? Oh boy…

Life as I know it turned 3 today!

I’ve been tumbling for three years? Oh boy…

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Mahatma Gandhi, as you know, walked barefoot all the time, and so his feet sported an impressive set of calluses. He also ate very little and so was rather frail, and his odd diet meant that his breath was not the most pleasant in the world. He was, then, a super calloused fragile mystic hexed by halitosis.

Tags: pun gandhi
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Chat
  • Question: Six kittens are playing together, three English kittens and three French kittens. The English kittens are names One, Two and Three. The French kittens are named Une, Deux and Trois. They decide to have a swimming competition as teams, across the stream in the back yard. Which team wins?
  • Answer: The English cats, 'cause Une Deux Trois quatre cinq.