Category Archives: Category Theory

Mathematical Aphorisms. Part 6.

It seems underemphasized that the parsimony of ZFC in the way of ‘types’ (having only one sort called sets) has the following practical and notational virtue: you can get by with a single type of the quantifier , and a … Continue reading

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Vignettes. Part 13.

There probably is no better illustration of the vagaries of notational fashion than the fact that nowadays, the numeral 1 is commonly used to denote the (conceptually very important) terminal category, while George Boole 170 years ago used 1┬áto denote … Continue reading

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Mathematical aphorisms. Part 4.

Bicategories are useful because they allow to constructively compare comparisons.

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Vignettes. Part 11.

There is a body of results in higher category theory which this expository blog post will present you a toy version of. Not to bias this post too much, and not to slight said body of results (they actually are … Continue reading

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Mathematical Aphorisms. Part 3.

With the discovery of higher dimensional algebra, the standard technical term linear equation accidentally has acquired a non-standard second meaning. In particular: old-sense linear equationnew-sense linear equationany old-sense equation.

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Vignettes. Part 8.

The following is an illustration of a very widely known, yet not widely-enough-known basic connection between things. Explanations will not be given. They can easily be found, given internet access. This connection gives a structure and systematic explanation for some … Continue reading

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Mathematical Aphorisms. Part 2.

One should intentionally take an intensional view on the things one cares about.

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