# 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.

**12**

**3**answers

### Does an H-space have at most one delooping?

**10**

**1**answer

### Finite complexes which are not Thom spectra

**3**

**0**answers

### Unstable and stable looping and delooping

**-2**

**1**answer

### Alternating property of H_2(T, Z)

**5**

**1**answer

### Quillen equivalent module categories

**9**

**1**answer

### Power operations from a Tate construction

**-1**

**1**answer

### Alternate property of H^2(T, Z) [on hold]

**3**

**1**answer

### Splitting of $H\mathbb{Z}$-module spectra

**1**

**1**answer

### The sheafification of taking cohomology is trivial?

**2**

**0**answers

### $E_\infty$-algebras and Tor-unital rings

**4**

**1**answer

### Link between homotopy equivalence of simplicial sets and categorical equivalences

**11**

**1**answer

### The homology of the orbit space

**23**

**1**answer

### Modern survey of unstable homotopy groups?

**5**

**2**answers

### Limit of weak equivalences in a Bousfield localization

**6**

**1**answer

### Precise reference for the equivalence of $E_n$ algebras and locally constant factorization algebra?

**2**

**0**answers

### Is there a definition of an unpointed schematic homotopy type?

**5**

**0**answers

### DG-Modules over CDG-algebras in the sense of rational homotopy theory

**1**

**0**answers

### Whitehead Theorem for maps

**2**

**0**answers

### resolution of differential graded algebras.

**16**

**3**answers

### Are there prominent examples of operads in schemes?

**13**

**0**answers

### How well-defined is $\bar\kappa$ in the stable $20$-stem?

**3**

**0**answers

### filetered colimit of fibrant-cofibrant objects

**5**

**1**answer

### On the existence of a domination map of a finite polyhedron

**14**

**1**answer

### Homotopy fixed points of complex conjugation on $BU(n)$

**11**

**1**answer

### homotopy and (co)filtered limits

**5**

**0**answers

### h-principle for pairs

**3**

**1**answer

### Making immersions from immersion conjecture into embeddings

**6**

**1**answer

### Unstable Greek letter elements

**7**

**0**answers

### What is this analog of $\mathbb A^1$ / proper homotopy theory?

**4**

**1**answer

### A finite Whitehead Theorem for $\infty$-topos

**8**

**1**answer

### How is topological André-Quillen homology (TAQ) a “stabilization”, exactly?

**8**

**1**answer

### Formality over $\mathbb{R}$ vs formality over $\mathbb{Q}$

**4**

**0**answers

### Quillen pair, fibrant-cofibrant objects

**1**

**0**answers

### Strict units in A-infinity algebras

**32**

**2**answers

### Why is Voevodsky's motivic homotopy theory 'the right' approach?

**3**

**0**answers

### Can a functorial factorization be modified so that it fixes the initial object?

**3**

**0**answers

### Monoidal equivalence of categories of modules in different models of higher algebra

**9**

**1**answer

### The structure of complex cobordism cohomology of the Eilenberg-Maclane spectrum

**10**

**1**answer

### Whitehead products in homotopy groups of spheres

**7**

**1**answer

### Reference request for K-Theory linearization

**2**

**1**answer

### $M$ is a manifold and isometrically embedded in $X$, homotopy type of $M$ is determined by polyhedrons $P$ s.t. $M\subseteq P \subseteq X$?

**5**

**2**answers

### Is the underlying vector space of the minimal model of an $A_{\infty}$-algebra canonical?

**2**

**1**answer

### Localization of a model category with respect to a class of maps

**11**

**1**answer

### Is there an expository account of homology of simplicial sets that does not assume prior familiarity with any variant of homology?

**13**

**1**answer

### Why $K(X) \longrightarrow G (X)$ is a Poincaré duality for K-theory?

**14**

**1**answer

### Spectra with “finite” homology and homotopy

**6**

**1**answer

### HKR generalized character theory question regarding a certain construction

**1**

**0**answers

### Maps having the right lifting property against cofibrations of compact spaces

**5**

**0**answers

### Homotopy functor calculus vs functor calculus in additive categories

**12**

**2**answers