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*Revision history:*

*- 2018 06 18: Removed an unhelpful paragraph.*

*- 2018 05 26 : First version.*

## Comments

`![picture](https://i.imgur.com/qTEaVos.png)`

I find that the "light cone" visualization helps to fix some of the inconsistencies:

This uses the Hasse diagram "smaller on bottom" order, but remains consistent with the standard symbols for "meet" and "join": the future light cone looks like a \(\vee\) for "least upper bound", and the past light cone looks like a \(\wedge\) for "greatest lower bound"). I still have to remember which symbol goes with which word, but things aren't quite so inconsistent from here.

(In other words, I don't interpret \(\vee\) and \(wedge\) as arrows, but as cones of light emanating from a flashlight. Think about the negative space around the symbol, rather than the symbol itself!)

This comes down to the defining property, where if "f" is a left adjoint to "g", then "f" appears on the

leftof the \(\le\): \(f(x) \le y \Leftrightarrow x \le g(y)\).`I find that the ["light cone"](https://en.wikipedia.org/wiki/Light_cone) visualization helps to fix some of the inconsistencies: <center>![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/470px-World_line.svg.png)</center> This uses the Hasse diagram "smaller on bottom" order, but remains consistent with the standard symbols for "meet" and "join": the future light cone looks like a \\(\vee\\) for "least upper bound", and the past light cone looks like a \\(\wedge\\) for "greatest lower bound"). I still have to remember which symbol goes with which word, but things aren't quite so inconsistent from here. (In other words, I don't interpret \\(\vee\\) and \\(wedge\\) as arrows, but as cones of light emanating from a flashlight. Think about the negative space around the symbol, rather than the symbol itself!) > I had a lousy time trying to memorize what made a "left adjoint" different from a "right adjoint". This comes down to the defining property, where if "f" is a left adjoint to "g", then "f" appears on the _left_ of the \\(\le\\): \\(f(x) \le y \Leftrightarrow x \le g(y)\\).`