#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Options

# PetePics Chapter 1 - Order terminology confusion

edited June 2018

Index of picture posts

Revision history:
- 2018 06 18: Removed an unhelpful paragraph.
- 2018 05 26 : First version.

• Options
1.
edited June 2018 Comment Source:![picture](https://i.imgur.com/qTEaVos.png)
• Options
2.
edited May 2018

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!)

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 $$\le$$: $$f(x) \le y \Leftrightarrow x \le g(y)$$.

Comment Source: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)\$$.