I print the following category theory cats as vinyl stickers.
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When I teach category theory in my abstract algebra classes, I give these stickers to my students. (As you can see, cat/opposite cat and infinity cat/tensor cat can be separated into two by a little gentle surgery.)
The original cat was tensor cat. In 2019, when Dan Rogalski (my PhD advisor) was on sabbatical in Seattle, he gave a series of lectures on tensor categories. These lectures were excellent, as I learned a lot about tensor categories and also doodled my new friend.
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In 2024, I participated in a workshop at SLMath (the artist formerly known as MSRI) and attended a series of lectures by Tobias Dyckheroff on infinity categories. During these lectures, infinity cat joined the party.
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If you would like some stickers, I’m happy to mail you some for a small fee to help defray costs ($1 per cat + the cost of an envelope and stamp). Send me an e-mail! Also let me know if you have thoughts on more cats—I have thoughts on higher cat and derived cat, but I haven’t yet made their acquaintance.
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Whenever I met one of them who seemed to me at all clear-sighted, I tried the experiment of showing him my Drawing Number One, which I have always kept. I would try to find out, so, if this was a person of true understanding. But, whoever it was, he, or she, would always say: “That is a hat.”
― The Little Prince, Antoine de Saint-Exupéry
Then I would never talk to that person about boa constrictors, or primeval forests, or stars. I would bring myself down to his level. I would talk to him about bridge, and golf, and politics, and neckties. And the grown-up would be greatly pleased to have met such a sensible man.