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Results tagged with homotopy-theory
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user 470393
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.
3
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3
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968
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Precise definition of the $\infty$-category of spaces, continuous maps, homotopies, homotopi...
I heard that there is an $\infty$-category $\mathbf{Top}_\infty$ whose objects are topological spaces, whose 1-morphisms are continuous maps, whose 2-morphisms are homotopies, whose 3-morphisms are ho …
- 91
5
votes
1
answer
251
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Example of a non-$\infty$-category whose homotopy category is a groupoid
What is an example of a simplicial set $S$ such that its homotopy category $hS$ is a groupoid, but such that $S$ is not an $\infty$-category?
I know that if $S$ is an $\infty$-category, then $S$ is a …
- 91