All Questions
Tagged with algebraic-k-theory simplicial-stuff
8 questions
12
votes
1
answer
429
views
Plus construction on Simplicial Sets?
I had asked this question in Math StackExchange a few days ago, but didn't get any answers. I believe its more suitable to be asked here.
Write $\mathsf{sSet}$ for the category of simplicial sets and $...
- 174
4
votes
0
answers
127
views
Almost acyclicity of the complex of configuration spaces of noncollinear points in projective plane over finite fields
Let $F$ be a finite field with many elements, say more than 7 for example, and $X$ be the corresponding projective plane $\mathbb{P}^2(F)$.
For a set of points in $X$, if any three of them are ...
- 441
23
votes
0
answers
647
views
Is this a model for $K$-theory of a triangulated category?
The recent question Complete the following sequence: point, triangle, octahedron, . . . in a dg-category reminded me of something I wanted to clarify long time ago; most likely this is now well known ...
- 18.4k
1
vote
1
answer
159
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homology of $B S^{-1} S$ computation in the proof that $+ = Q$
Let $S$ denote the category of projective (left) $R$-modules with isomorphisms for arrows. We have that
$BS^{-1}S \sim B \text{GL}(R)^+ \times K_0(R)$
In proving this, in Srinivas' algebraic K-...
- 1,105
1
vote
1
answer
309
views
Simplicial sets from bisimplicial sets, and their realisations.
From a bisimplicial space $T$, one can consider the simplicial spaces $\underline p \mapsto T_{pp} $, $\underline p \mapsto |\underline q \mapsto T_{pq} |$, and $\underline q \mapsto |\underline p \...
- 1,105
3
votes
0
answers
365
views
Are connected categories with pullbacks weakly contractible?
Quillen's Theorem A says that a functor between (small) categories $f:I\rightarrow J$ induces a weak equivalence of the nerves if for each $j\in J$ the comma category $f/j$ is weakly contractible. In ...
- 1,138
1
vote
1
answer
769
views
Nerves of simplicial objects in categories/Waldhausen's S-construction
Is there a good nerve-like functor from simplicial objects in categories to simplicial sets which takes level-wise equivalences of categories to weak equivalences?
To give this some context, I'd ...
- 1,138
6
votes
1
answer
1k
views
Geometric Realization of a Simplicial Category
Let $S:\varDelta^{op}\to (cat)$ be a functor where the category on the right is the category whose objects are categories with cofibrations and morphisms are exact functors(from Waldhausen's paper, ...
- 1,553