Tag Archives: category theory

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Categorial decomposition of Galilean spacetime. Sean Carroll tells us that it was Galileo who first si rese conto che motion can be separated into: motion in the x direction — ẋ or x′[t] motion in the y direction — ẏ or y′[t] motion … Continue reading

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Category Theory for Programmers redraw pictures of ƒ(A)=B so that the morphisms look like • and the objects look like →. Hey, why not? string diagrams (process networks) are just as good as algebraic symbology associativity tensor products if switch( … Continue reading

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The definition of toposes has surprisingly powerful consequences. (For example, toposes have all finite colimits.) Probably the best analogy elsewhere in which a couple of mild-sounding hypotheses pick out a very narrow and interesting class of examples is the way … Continue reading

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The existential quantifier ∃ of logic (the propositional calculus) and the image operation along a continuous function ƒ from topology turn out to be essentially the same operation: from a categorical point of view they are both adjoint functors. Steve … Continue reading

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http://www.cs.ox.ac.uk/quantum/talksarchive/clap1/clap1-chrisisham.avi Is there really such a thing as a point? Well, not really…. Ask any of our undergraduates, why the real numbers? Can you say there’s something √π centimetres away from here?—Well, not really, it’s an approximation….—An approximation to what? “We’re not … Continue reading

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The theory of universal algebras was well-developed in the twentieth century. [It] provides a basis for model theory, and [provides] an abstract understanding of familiar principles of induction, recursion, and freeness. The theory of coalgebras is considerably [less] developed. Coalgebras … Continue reading

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“Have you ever done acid, kid? This book is like Acid.” —John L. Rhodes, speaking of the book Topos Theory by Peter Johnstone (Source: http://www.amazon.com/gp/product/0521337798?ie=UTF8&tag=hiremebecauim-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0521337798)

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