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Operations and Lawvere theories
Groups are in particular sets equipped with two operations: a binary operation (the group operation) and a unary operation (inverse) . Using these two operations, we can build up many other operations,...
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A puzzle about operations
Previously we described -ary operations on (the underlying sets of the objects of) a concrete category , which we defined as the natural transformations . Puzzle: What are the -ary operations on finite...
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Operations, pro-objects, and Grothendieck’s Galois theory
Previously we looked at several examples of -ary operations on concrete categories . In every example except two, was a representable functor and had finite coproducts, which made determining the -ary...
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Cantor’s theorem, the prisoner’s dilemma, and the halting problem
Cantor’s theorem is somewhat infamous as a mathematical result that many non-mathematicians have a hard time believing. Trying to disprove Cantor’s theorem is a popular hobby among students and cranks;...
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