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Results tagged with homotopy-theory
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user 35183
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.
5
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answers
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Refined cofinality theorem for homotopy limits of spaces
If $C$ is a simplicial model category, $F\colon I\longrightarrow J$ a functor between small categories, and $X\colon J\longrightarrow C$ a diagram, the canonical map $holim_JX\longrightarrow holim_IX\ …
- 425
7
votes
1
answer
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Finite homotopy limits commute with sequential homotopy colimits
I would like to know for what kind of model category finite homotopy limits commute with sequential homotopy colimits. Would cofibrantly generated and finitely locally presentable be enough? It seems …
- 425
1
vote
The classifying space of an infinite totally ordered set is contractible
I am not sure if you consider this explicit, but here you go:
Choose a point $x_0\in X$, and let $F\colon X\to X$ be the functor that sends $x$ to itself if $x\geq x_0$, and to $x_0$ otherwise. There …
- 425