# Tag Info

### Short exact sequences every mathematician should know

There is one obvious sequence that underlies all vector analysis and a lot that builds up on it, no matter if its applied analysis, PDE, physics or the original foundations of algebraic topology. Yet ...

### Short exact sequences every mathematician should know

The exponential sheaf sequence: $$0\to 2\pi i\,\mathbb Z \to \mathcal O_M {\buildrel\exp\over\to}\mathcal O_M^*\to 0$$ where $\mathcal O_M$ is the sheaf of holomorphic functions on the complex ...

Accepted

### What are the "correct" conventions for defining Clifford algebras?

This is not really an answer, but rather a meta-answer as to why there exist many conventions in the first place. The symmetric monoidal category $\mathit{sVect}$ of super-vector spaces has a non-...
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### Understanding a quip from Gian-Carlo Rota

I think Abdelmalek Abdesselam and William Stagner are completely correct in their interpretation of the words "Behind" and "one immutable source" as describing one theory, the theory of symmetric ...
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### Morava K-theories for dummies?

This is a result in algebraic topology, where we study the structure of topological spaces $X$. One early way to do this is to calculate a thing called $H_*(X)$, the ordinary homology of $X$. Later ...
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Perhaps one of the biggest ideas that VV was pursuing is the Initiality Conjecture for Martin-Löf type theory (with universes). A rough idea is that from the rules for a type theory, one can define a ...

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### Short exact sequences every mathematician should know

I suppose many algebraic topologists would agree that the short exact sequence $$0\longrightarrow \mathbb Z/p \longrightarrow \mathbb Z/p^2 \longrightarrow \mathbb Z/p\longrightarrow 0$$ giving rise ...

### The $K$-theory homology of the Eilenberg-MacLane spectrum

We have $KU_*(H\mathbb Z) = \pi_*(KU\wedge H\mathbb Z)$; this ring is concentrated in even dimensions and carries an isomorphism between the additive and multiplicative formal group law, hence is ...
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### Why does K-theory need schemes to be Noetherian?

You don't need the Noetherianness hypothesis to talk about K-theory. But the definition you propose in your question is not suited for the most general case. From a notion of K-theory we want at least ...
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### Problems concerning subspaces of $M_{n}(\mathbb{Q})$

Let's call this maximal dimension function $\rho_{\mathbb{Q}}:\mathbb{N}\to\mathbb{N}$, i.e., $\rho_{\mathbb{Q}}(n)$ is the largest possible dimension of a subspace $N\subset M_n(\mathbb{Q})$ such ...
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### The $K$-theory homology of the Eilenberg-MacLane spectrum
Since for any two spectra $E,F$ we have $$E_n(F)=[\mathbb{S}^n,E\wedge F]\cong [\mathbb{S}^n,F\wedge E] = F_n(E),$$ you may as well ask about $H_n(KU;\mathbb{Z})$, the integral homology of the ...