In search of the pythagorean tensor
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In 1973, Lawvere showed that metric spaces can be regarded as enriched categories, enabling a fruitful backandforth between metric geometry and category theory. But one part of metric geometry whose categorical counterpart has never been found is the “Pythagorean tensor” – essentially, the formula sqrt(x^{2}+y^{2}), fundamental to Euclidean geometry. I will describe a partially successful attempt to solve this problem.
This talk is part of the Category Theory Seminar series.
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