Category Archives: Mathematics

Higher Trees Today. Part 0.

For the time being, the installments of the serial ‘Higher Trees Today’ will focus on three kinds of higher trees: Contractible Spaces of Choices (c.s.c.) Diestel–Oum decompositions (d.o.d.) Kalai trees (k.t.) Masbaum-Vaintrob trees (m.v.t.) Of course, while the latter three … Continue reading

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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┬áto denote … Continue reading

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Vignettes. Part 12.

Did you know that mathematics will provide you with more-or-less standardized tools to usefully express commonly-occurring ideas? For exaple, the following illustration contains at least three examples of this: (0) the symbol for boundaries of things, the symbol to symbolize … 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 9. Two different meanings of “star hypergraph”.

This little post is meant to be technically useful, pointing out one of the myriad clashes of terminology that exist in just about any science. I happenend to know the term “star hypergraph” for a long time, but only in … Continue reading

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