# Questions tagged [homotopy-theory]

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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### $\infty$-categorical understanding of Bridgeland stability conditions?

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### A homotopy problem for morphisms of dg-algebras

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### What are the advantages of simplicial model categories over non-simplicial ones?

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### Does Ex^∞ send homotopy inverse limits of ∞-categories to homotopy inverse limits of spaces

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### The table reduction morphism of operads from Barratt-Eccles to Surjection

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### Iterated free infinite loop spaces

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### Construction of a $K(\pi,1)$-space?

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### Two models for the classifying space of a subgroup via the geometric bar construction

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### Extension of sheaves of $\infty$-algebras

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### Tensor product of an L-infinity algebra with the cochains on the 1-simplex

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### References on $HZR$ theory

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### $\Gamma$-sets vs $\Gamma$-spaces

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### Homology of the fiber

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### $X \rtimes Y \simeq X \vee (X \wedge Y)$ for $X$ a co-H-Space

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