All Questions
13 questions
8
votes
0
answers
256
views
(Reduced) cyclic homology of a free product of unital algebras
Shameless upfloat of 1-year old question - the motivation is that in general the corresponding Banach version is false, so I am trying to see where the proof breaks down, and what (if anything) can be ...
- 25.8k
7
votes
0
answers
116
views
A "lower-central" filtration of Steenrod algebra?
$\renewcommand{\Atwo}{\mathcal{A}_2}$ So, a lot of good work has been accomplished by filtering the Steenrod algebras $\mathcal{A}_p$ in powers of the Augmentation ideal; For reasons partly ...
- 731
6
votes
2
answers
684
views
Somewhat general question that includes: "Do quasi-isomorphic cdgas have quasi-isomorphic spaces of derivations?"
Question: Given two quasi-isomorphic dg commutative algebras (over a field of characteristic zero, if you like), to what extent do their various homological geometric data agree?
Example: Given a dg ...
- 54.6k
6
votes
1
answer
241
views
For which exact couples do associated spectral sequences degenerate at $E_1$?
It is well known that a bigraded exact couple of objects of an abelian category yields a spectral sequence (cf. https://ncatlab.org/nlab/show/exact+couple#SpectralSequencesFromExactCouples). My ...
- 16.9k
6
votes
1
answer
623
views
On various "extension closures" and "orthogonals" in triangulated categories
A vague form of my question is the following one: for a class of objects $D$ of a triangulated category $C$ we consider the class $E$ of objects that satisfy $Mor_{C}(d,e)=\{0\}\ \forall d\in D$; ...
- 16.9k
5
votes
0
answers
520
views
Spectral sequences coming from filtrations (Postnikov systems) in triangulated categories: references and convergence
Let $c^i: M^{\ge i+1}\to M^{\ge i}$ for $i\in \mathbb{Z}$ be an sequence of morphisms in a triangulated category $C$ and assume that $M^{\ge i}$ are equipped with compatible morphisms into an object $...
- 16.9k
5
votes
0
answers
225
views
Can triangulated categories be "approximated by countable subcategories" (that are triangulated but not full!)?
For a given (finite) set of (objects and) morphisms $f_i$ in a triangulated category $C$ I am interested in a (non-full!) triangulated subcategory $C'\subset C$ of "small size" that would contain them....
- 16.9k
4
votes
1
answer
259
views
Induced map in K-theory by a "trivial" bimodule
Let $R$ be a ring (not necessary commutative) and let $P_{\bullet}$ be a perfect $R$-bimodule (chain complex). I will denote the category of perfect right $R$-chain complexes by $\textbf{Perf}(R)$. ...
- 43
3
votes
0
answers
180
views
$k$-invariants of $KO$ and $ko$ and differentials in the AHSS spectral sequence
Let $KO$ and $ko$ denote real $K$-theory and connective real $K$-theory. It appears to be a well done result that the $k$-invariants can be used to determine the early differentials in the Atiyah-...
- 855
3
votes
0
answers
188
views
Can one complete a morphism of commutative triangles to a "commutative cube" in a triangulated category?
This question is a continuation of Can one extend a morphism of commutative triangles to a morphism of octahedral diagrams?.
I am deeply grateful for the contributions there; they roughly say that ...
- 16.9k
1
vote
0
answers
124
views
Computing the induced homomorphisms of derived functors using acyclic resolutions
Let's suppose that $F\colon \mathcal A\to \mathcal B$ is a right exact additive functor between abelian categories such that $\mathcal A$ has enough projectives. Standard references shows that if $Q_\...
- 38.6k
1
vote
0
answers
83
views
Hochschild homology computation of certain type
I know that in general Hochschild homology is not very computable. However, this certain type of Hoshschild homology shows up and I feel like there could be existing result.
Let $k$ be a field and $A$ ...
- 449
1
vote
0
answers
70
views
On (universal) additive functors making a given complex contractible: examples?
Let $M=(M^i)$ be a (cohomological) complex of objects of some additive category $A$ (I am mostly interested in "short" complexes; yet one may also consider an unbounded $M$). I am interested in those ...
- 16.9k