Monthly Archives: August 2017

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

Posted in expository, Higher trees, Mathematics, News, Olds, Research, Silviculture, Simplicial complexes, Structure theory | Leave a comment

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

Posted in Category Theory, expository, mathematical aphorisms, Mathematics, Olds | Leave a comment

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

Posted in digraph theory, expository, Mathematics, Olds, Research, Technology. | Leave a comment

Mathematical Aphorisms. Part 5.

One should not pool together concepts, rather one should pull together concepts.

Posted in expository, mathematical aphorisms, Olds | Leave a comment

Mathematical aphorisms. Part 4.

Bicategories are useful because they allow to constructively compare comparisons.

Posted in Category Theory, expository, mathematical aphorisms, Mathematics | Leave a comment

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 | Leave a comment

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.

Posted in Category Theory, expository, mathematical aphorisms, Mathematics | Leave a comment