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To me it looks like a simple theory made needlessly harder by bad UX design. For instance, arrows are written left to right as f: X -> Y, g: Y -> Z, and compose
by abecedarius 10y ago
To me it looks like a simple theory made needlessly harder by bad UX design. For instance, arrows are written left to right as f: X -> Y, g: Y -> Z, and composed right to left, g . f. There a lot of unmnemonic names like epic and monic morphisms, which are dual to each other but with unrelated names. The beginner, at least if they're me, must struggle to fit all these difficulties into their head together long enough to even follow what's being claimed, before they can work with the formalism.
If category theory is as cool as it sounds (and as simple as it doesn't) then somebody could do us a neat service by working out a game like http://worrydream.com/AlligatorEggs/ http://worrydream.com/AlligatorEggs/ did for the lambda calculus. (Added: I guess it must've already been done, as formalizations of category theory in interactive proof assistants. Any tips on what's the most accessible?)
- harveywi 10y agoWhen I look at category theory diagrams, I always think that the visual embedding is underutilized. It seems like the diagrams could be enriched with more symbols to encode more information. For example (and probably a bad example) differentiating between automorphisms and identity functions using different symbols on their arrows). Somehow making these diagrams completely self-contained could be potentially interesting, and I wonder what the tradeoffs would be. Maybe the current formulation of the diagrams is just right for people who use them to do a lot of heavy lifting. It would be interesting to hear some opinions on this.
- bitdiddle 10y agoYou might have a look at section 1.39 in "Categories, Allegories", by Freyd and Scedrov. They introduce a language of diagrams and show how common definitions can be represented this way. Not a particularly easy read.