# Tagged Questions

**8**

votes

**0**answers

212 views

### Nonunital $E_\infty$-rings

An elementary fact of algebra is that the category of nonunital commutative rings is equivalent to that of $\mathbb{Z}$-augmented unital commutative rings, the equivalence being given by forming ...

**6**

votes

**0**answers

206 views

### Topological quotient Hopf-algebras and “change-of-rings”

One way of constructing coalgebra objects in the homotopy theorist's category of spectra is to take the suspension spectrum of a space, with the diagonal providing a cocommutative comultiplication. ...

**9**

votes

**1**answer

577 views

### I think I have a category enriched in $(\infty,n-1)$-categories. Is it an $(\infty,n)$-category?

I have recently been thinking about some mathematical gadgetry that should together combine into an $(\infty,n)$-category (actually, an $(n,n)$-category) for $n = 4$. I don't know what axioms I need ...

**3**

votes

**0**answers

104 views

### understanding the definition of $\infty$-operad of module objects

I'm just trying to understand the following definition:
Definition 3.3.3.8 in Higher Algebra by J. Lurie defines the $\infty$-operad of $O$-module objects, and says the following:
Let $O^\otimes$ be ...

**5**

votes

**0**answers

106 views

### Reference for a generalization of Γ-spaces to monoidal model categories

Γ-spaces were introduced by Segal in 1969 as models for what can be now described
as commutative ∞-monoids and ∞-groups in cartesian symmetric monoidal ∞-categories, e.g., E_∞-spaces and connective ...

**5**

votes

**1**answer

519 views

### Can motivic E_∞-ring spectra be strictified to commutative motivic symmetric ring spectra?

Theorem 4.4.4.7 in Lurie's Higher Algebra (or Theorem 4.3.22 in DAG III) states (roughly speaking) that under certain conditions
the ∞-category of commutative ∞-monoids in a given symmetric monoidal ...

**4**

votes

**1**answer

482 views

### Topological Hochschild cohomology?

Let $A$ be a $E_\infty$-ring spectrum. By EKMM, it may be treated as a commutative algebra in the appropriate category. In particular, one may define topological Hochschild homology as ...

**21**

votes

**2**answers

1k views

### generalisations of the Seifert-van Kampen Theorem?

I have been reading Jacob Lurie's book "Higher Algebra", version May 8, 2011. One is grateful to him for covering such a lot of ground and for making it all so readily available.
My attention was ...

**3**

votes

**1**answer

380 views

### $A_{\infty}$ structure questions

Hello,
I would like explanation or clear source for some things related to $A_{\infty}$-spaces, via Stasheff's polytopes.
I tried not to think about them, because they seem too complicated for me; I ...