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Donald Yau and I have a new book out! 
It's called "Homotopy Theory of Enriched Mackey Functors", and I want to explain what those words mean!
https://arxiv.org/abs/2212.04276
[thread about #HomotopyTheory, #CategoryTheory, and #Mackey functors]
(0/11)
Actually, the first thing I want to say is how much I enjoy working with Donald. Here's a picture of him looking out for me when I was a new faculty member at OSUN [1]. I've learned a lot of math, and a lot about *doing* math through our work. We've got more things coming down the pike, but that's for another day. :)
[1] https://mathstodon.xyz/@weaniejeanie53@mas.to/109400557209350472
(1/11)
Thanks for reading!
If you're curious about more, go ahead and check out the book.
https://arxiv.org/abs/2212.04276
We have lots of background, cross-referencing, and outlining. As per usual, you won't find us skipping any explanations with words like "easy", "obvious", etc. And if you have questions, let me know!!
p.s. The decorations on that last diagram made me think of the cool moss and lichen growing on this rock at my house
(11/11)
@nilesjohnson Are there any particular sections I should look at if I'm primarily interested in G-spectra?
@siddharth64 That's a very good question, but really this book is more like *adjacent* to equivariant homotopy instead of *about* it. The Guillou-May theorem in chapter 0 says that G-spectra have the same homotopy theory as Mackey functors, but the proof is nontrivial and we don't include it. Instead, we take that as a starting point and focus on the homotopy theory of the Mackey functor categories.
@nilesjohnson oh wow, another one! Congratulations! How many is it now? ;)
@emilyriehl this is our third together, so far... :)