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Counting Is HardI've kind of always wondered what the point of definitions like a group is a non-empty set \(G\) with a binary operation \(d\) satisfying \(d(d(d(z,d(x, d(x,x))),d(z,d(y,d(x,x)))),x) = y\) is, other than because we can, but <a href="https://math.stackexchange.com/a/4366021" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://math.stackexchange.com/a/4366021</a> offers one such answer in terms of homotopy type<a href="https://mathstodon.xyz/tags/grouptheory" class="mention hashtag" rel="tag">#grouptheory</a> <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="tag">#categorytheory</a> <a href="https://mathstodon.xyz/tags/homotopytheory" class="mention hashtag" rel="tag">#homotopytheory</a>

183231bcbStable homotopy theory implies the existence of release candidate homotopy theory, beta homotopy theory, and alpha homotopy theory. (How long before a homotopy theorist tells me these are actual things?) <a href="https://transfem.social/tags/HomotopyTheory" rel="nofollow noopener noreferrer" target="_blank">#HomotopyTheory</a> <a href="https://transfem.social/tags/StableHomotopyTheory" rel="nofollow noopener noreferrer" target="_blank">#StableHomotopyTheory</a>

RanaldCloustonMy <a href="https://fediscience.org/tags/blog" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#blog</a> this week is on the Blakers-Massey theorem, whose proof in homotopy type theory <a href="https://fediscience.org/tags/HoTT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HoTT</a> is one of the key achievements of that community. <a href="https://blogs.fediscience.org/the-updated-scholar/2024/03/15/discussing-a-mechanization-of-the-blakers-massey-connectivity-theorem-in-homotopy-type-theory/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://blogs.fediscience.org/the-updated-scholar/2024/03/15/discussing-a-mechanization-of-the-blakers-massey-connectivity-theorem-in-homotopy-type-theory/</a> <a href="https://fediscience.org/tags/TypeTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TypeTheory</a> <a href="https://fediscience.org/tags/HomotopyTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HomotopyTheory</a>

Niles JohnsonDonald 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!<a href="https://arxiv.org/abs/2212.04276" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://arxiv.org/abs/2212.04276</a>[thread about <a href="https://mathstodon.xyz/tags/HomotopyTheory" class="mention hashtag" rel="tag">#HomotopyTheory</a>, <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="tag">#CategoryTheory</a>, and <a href="https://mathstodon.xyz/tags/Mackey" class="mention hashtag" rel="tag">#Mackey</a> functors](0/11)

JonathanNew paper from the indomitable Ze Wong and myself. "The Operadic Nerve, Relative Nerve, and the Grothendieck Construction" <a href="https://arxiv.org/abs/1808.08020" rel="nofollow noopener noreferrer" target="_blank">https://arxiv.org/abs/1808.08020</a> <a href="https://scholar.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://scholar.social/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#categorytheory</a> <a href="https://scholar.social/tags/homotopytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#homotopytheory</a>

JonathanHey y'all, I'm a postdoc in <a href="https://scholar.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a>. I study <a href="https://scholar.social/tags/topology" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#topology</a> <a href="https://scholar.social/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#categorytheory</a> <a href="https://scholar.social/tags/homotopytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#homotopytheory</a> and the scary sounding ∞-categories! Also excited about increasing representation in mathematics of trans people, women and people of color. Also involved in setting up the <a href="https://scholar.social/tags/postdoc" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#postdoc</a> <a href="https://scholar.social/tags/union" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#union</a> here at the University of Washington. Currently located in <a href="https://scholar.social/tags/seattle" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#seattle</a> but will probably be relocating in the next year because that's <a href="https://scholar.social/tags/postdoclife" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#postdoclife</a>. <a href="https://scholar.social/tags/introduction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#introduction</a>

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