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A thread for general comments or suggestions on my series of picture posts for John's 2018 Applied category theory course.

Some feedback I'd particularly welcome:

**Errors.**I made various mistakes while putting these together. I think everything's correct now, but please let me know of any false statements.**Use of images.**I tried to size the images and the fonts so that it would look roughly the same as a post on the forums. Since images are totally inflexible, some problems may arise. Is the font size large enough to read clearly? Are the images unpleasant to use, e.g. on mobile? Is being locked into the white background I chose really irritating?**Narrowness.**All my intuition on this material so far comes from finite sets. If the things I say are incomplete, misleading, or incorrect in the wider world of orders, I appreciate being corrected. Similarly, much of the stuff I wrote may only be true for posets, not preorders, which again may mean that my focus was in the wrong places.

It's a hassle to update the images, but I do want to fix any problems if possible.

## Comments

These are great! I feel like I'm getting a better intuition for everything from taking another pass over the material with your picture posts. I'm excited to see what you might turn out for the later chapters :)

For what it's worth, I especially liked your exploration of the relation \({\trianglelefteq} \subseteq P \times Q\). I thought that really brought a new angle on what Galois connections are made of.

`These are great! I feel like I'm getting a better intuition for everything from taking another pass over the material with your picture posts. I'm excited to see what you might turn out for the later chapters :) For what it's worth, I especially liked your exploration of the relation \\({\trianglelefteq} \subseteq P \times Q\\). I thought that really brought a new angle on what Galois connections are made of.`

Thanks Jonathan! I was kind of worried about including that relation. It grew into quite a large detour, and I didn't want the amount of text to discourage anyone from continuing to the last post, which is my favorite of the series.

I did want to see how uniformly I could treat the monotonicity and adjunction conditions, so I included it anyway. It may not be that practical, but I'm glad to know someone besides me found it interesting.

`Thanks Jonathan! I was kind of worried about including that relation. It grew into quite a large detour, and I didn't want the amount of text to discourage anyone from continuing to the last post, which is my favorite of the series. I did want to see how uniformly I could treat the monotonicity and adjunction conditions, so I included it anyway. It may not be that practical, but I'm glad to know someone besides me found it interesting.`

Pete these look great! Thanks for making them.

`Pete these look great! Thanks for making them.`

I'm doing the same as Jonathan. Very helpful to someone whose mathematical education is insufficient for a class like this.

Thanks again, Pete!

`I'm doing the same as [Jonathan](https://forum.azimuthproject.org/discussion/comment/18618/#Comment_18618). Very helpful to someone whose mathematical education is insufficient for a class like this. Thanks again, Pete!`

Thank you Pete! I started late and your pictures were of great help in understanding adjoints. Especially the visual representation on placing isomorphic elements on top of each other or having hatched arrow to differenciate left adjoints from right adjoints was great!

`Thank you Pete! I started late and your pictures were of great help in understanding adjoints. Especially the visual representation on placing isomorphic elements on top of each other or having hatched arrow to differenciate left adjoints from right adjoints was great!`