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Results tagged with homotopy-theory
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user 42658
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
10
votes
1
answer
287
views
Criterion for homotopy pullback square of simplicial categories
Assume given a pullback square of simplicial categories
$$\begin{array}[c]{ccc}
A&{\rightarrow}&B\\
\downarrow&&\downarrow\\
C&{\rightarrow}&D.
\end{array}$$
Suppose further that one of the induced …
- 660
7
votes
Why do we need model categories?
Extensive answers have already been given in this thread. Just a few remarks here and there.
I think the question “why we need” assumes something about “we”, and in some extent, about “need”. There …
- 660
5
votes
Derivators and fibred $\infty$-categories
I am no Denis-Charles but given the other paper you quoted let me think of a sketch, perhaps you will be able to make the right out of it.
Let $\mathcal E \to \mathcal C$ be a Quillen presheaf (model …
- 660