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Results tagged with homotopy-theory
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user 4008
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.
11
votes
Accepted
Group Completions and Infinite-Loop Spaces
A well-written discussion of the group completion can be found on pp. 89--95 of
J.F. Adam: Infinite loop spaces, Ann. of Math. studies 90 (even though he only
discusses a particular group completion o …
- 22.6k
9
votes
Splitting of the Universal Coefficients sequence
I would claim that the splitting (and indeed the whole universal coefficient
theorem) is not really a topological theorem. If we take the homological version
one really works with the chain complex $C …
- 22.6k
5
votes
An explicit description of Lawvere's segment in the category of simplicial sets
The value of $L$ on the element $[n]\in\Delta$ is, by Yoneda's lemma, equal to
the set of morphisms $[n]\rightarrow L$, i.e., the set of subobjects of $[n]$.
Such a subobject $S$ is generated by the n …
- 22.6k