Category Archives: Category Theory

Mathematical Aphorisms. Part 6.

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 to 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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Vignettes. Part 6.

If one cares for categories, one should intentionally take an intensional view on them:  axioms matter. In particular, associativity is an axiom. But it is excusable that one sometimes forgets that associativity is axiomatic: so many categories are concretizable (and then, … Continue reading

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