Small Eyes Notation

Adapted from the preface of "Coend Calculus", a paper on category theory by Fosco Loregian:

http://zhurnaly.com/images/eyes-wide-with-fear.png"Some of the exercises are marked with a symbol <<eyes wide with fear>> — this means they are more difficult and less well-posed questions than the others. This can happen on purpose (and thus part of the exercise is understanding what the question is) or not (and thus the question and its answer are not completely clear even to the author). In this second case, it is likely that a complete answer might result in new Mathematics that we'd be happy to expand with the solvers."
http://zhurnaly.com/images/eyes-looking-up.png"Other kinds of 'small eyes' are present along the book: the paragraphs decorated with <<eyes looking up>> contain material that can be skipped at first reading, or material that deepens a prior topic in a not-so-interesting detour."
http://zhurnaly.com/images/eyes-looking-right.png"<<eyes looking right>> is used to signal key remarks and more generally important material that we ask the reader to digest properly and analyse in full detail. "

Loregian comments:

The author learned this funny notation during his freshman year, when he was handed [a text by G. De Marco] for the first time; the "small-eyes" notation accompanied me throughout all my mathematical life until today. In [De Marco] this notation has the following meaning: various facial expressions explain the different ways the reader is supposed to behave when they meet them: <<eyes looking up>>, abstract material; <<eyes looking down>>, standard exercises; <<eyes looking right>>, material that you are supposed to meditate a lot; <<eyes wide open>>, shattering exercises.

(cf Good Notation (2001-01-06), Bra Ket (2001-01-24), Stokes Theorem (2006-01-27), Useful Doodles (2019-12-10), ...) - ^z - 2020-02-22