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Category Archives: expository
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.) MasbaumVaintrob trees (m.v.t.) Of course, while the latter three … Continue reading
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
Vignettes. Part 12.
Did you know that mathematics will provide you with moreorless standardized tools to usefully express commonlyoccurring 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
Posted in digraph theory, expository, Mathematics, Olds, Research, Technology.
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Mathematical Aphorisms. Part 5.
One should not pool together concepts, rather one should pull together concepts.
Posted in expository, mathematical aphorisms, Olds
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Mathematical aphorisms. Part 4.
Bicategories are useful because they allow to constructively compare comparisons.
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
Posted in Category Theory, expository, logic, Mathematics, Olds
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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 nonstandard second meaning. In particular: oldsense linear equationnewsense linear equationany oldsense equation.