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Results tagged with higher-category-theory
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user 75
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
17
votes
Homotopy-theoretic derived Morita equivalences
Fernando's answer is excellent, but I can't resist mentioning what is perhaps the simplest counterexample to a generalization to your question. As Fernando says, there are counterexamples if you gene …
- 31.2k
9
votes
Accepted
Is a conservative finite limit preserving functor of (infinity,1)-categories homotopically f...
Here's a counterexample. Let $\mathcal{C}=\mathcal{D}$ be the stable $(\infty,1)$-category of perfect complexes over $\mathbb{Z}_{(p)}$, and let $F(X)=X\otimes \mathbb{Z}/p$ (the derived tensor produ …
- 31.2k
8
votes
Accepted
Homotopy factorization of morphisms of chain complexes
Consider the following diagram in which the rows are cofiber sequences:
$$\require{AMScd}\begin{CD}
\tau_{\geq0}A @>>> A @>>> \tau_{\leq-1}A @>>>\Sigma\tau_{\geq0}A\\
@VVV @VVV @| @VVV\\
\tau_{\geq0}B …
- 31.2k
25
votes
Accepted
Are Thom spectra MU, MSO and K-theory spectra KU, KO modules over some truncations of the sp...
For any $k$ and any $0<n<\infty$, $K(n)\wedge \pi_{\leq k}S=0$. Indeed, this is true for any spectrum with finitely many homotopy groups, since $K(n)\wedge H\mathbb{Z}=0$ and any such spectrum has a …
- 31.2k