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Results tagged with homotopy-theory
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user 84398
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.
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A map that names itself
Call the walking arrow $\Delta_{1}$, containing exactly one nontrivial 1-cell $[0<1] : 0 \to 1$. I am interested in a map $\Phi : \Delta_{1} \to \mathrm{Type}$, such that $\Phi [0<1] = \Phi$ (and ther …
- 12.9k
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"Boundaries" in Free Simplicial Monoids
I suspect that this has been addressed somewhere already, but I cannot find anything. Let $\hat{\Delta}$ denote simplicial sets, and $Mon\hat{\Delta}$ simplicial monoids. There is a forgetful functor …
- 713
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Fundamental monoid pertaining to adjunctions
Marco Grandis has been working to collect and formalize the ideas of directed homotopy theory (his main work on the subject has been listed in the references at the nLab page on the subject: directed …
- 713
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Underdetermined Polynomial $(\infty ,1)$-Functors
Is there any sense in which the full subcategory of n-excisive functors (on spectra or on pointed spaces) on those functors $F$ which satisfy a set of distinct (modulo homotopy equivalence) equations …
- 713
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Homotopic version of Freyd's AT category observations
Freyd was the first to formalize a striking comparison between abelian categories and topoi, showing that their exactness properties can be jointly captured by the axioms of AT categories, and the dif …
- 713