Skip to main content

All Questions

Filter by
Sorted by
Tagged with
13 votes
3 answers
978 views

Model Structure/Homotopy Pushouts in topological monoids?

Let $\mathsf C$ be the category of topological monoids, that is, the category of monoids in $(\textsf{Top}, \times)$. Can the model category structure on $\textsf{Top}$ (Serre fibrations, ...
6 votes
1 answer
622 views

When is the cofibrant replacement of a product the product of the cofibrant replacements?

I'm in a situation where I'd like to prove $Q(E\otimes E) \simeq QE \otimes QE$ for a monoid $E$ in a symmetric monoidal model category. I know it's not true in general that $Q(E\otimes F)\simeq QE \...
3 votes
1 answer
161 views

Are cofibrations in topological monoids preserved by forming the product with the identity?

Consider the category $\mathrm{Mon}(\mathbf{Top})$ of topological monoids, together with the model structure transferred along the adjunction $F:\mathbf{Top}\rightleftarrows \mathrm{Mon}(\mathbf{Top}):...
10 votes
1 answer
440 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 ...
10 votes
2 answers
1k views

Connective spectra versus simplicial abelian groups - very basic question

Hello, I have very general , "introductory" questions (It is quite hard for me to seek for specific things in the algebraic topology literature). I guess that connective spectra have a model ...