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Results tagged with homotopy-theory
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user 121009
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.
11
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0
answers
299
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Is there a homotopy coherent analogue of Dieudonné modules?
Let $K$ be a perfect field with characteristic $>0$ and $\mathcal{H}$ the category of graded connected abelian hopf algebras over $K$.
By a theorem of Schoeller there is a canonical equivalence betwee …
- 1,361
5
votes
1
answer
433
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Tensor product of coaugmented conilpotent coalgebras
Let $\mathbb{K}$ be a field of char. 0.
Let $\mathrm{A}, \mathrm{B}$ be conilpotent cocommutative coaugmented counital dg-coalgebras over $\mathbb{K}$
(i.e. that their corresponding cokernel of their …
- 1,361
10
votes
1
answer
305
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Is every symmetric monoidal combinatorial model category symmetric monoidally Quillen equiva...
Is every symmetric monoidal combinatorial model category symmetric monoidally Quillen equivalent (by a zig-zag of symmetric monoidal Quillen equivalences)
to a symmetric monoidal combinatorial simpli …
- 1,361
3
votes
0
answers
107
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Inverse limit of chains of Eilenberg Mac Lane spaces
Let $... \to G_2 \to G_1$ an inverse system of abelian groups with inverse limit $G$, let $n \geq 2$ and $F$ a field. The induced inverse system $$... \to C_*(K(G_2,n);F) \to C_*(K(G_1,n);F) \ (*)$$
o …
- 1,361
4
votes
0
answers
61
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Full subcategories of stable $\infty$-categories closed under all shifts
Is there a name for an $\infty$-category C that admits a zero object and suspensions such that the suspension functor $C \to C$ is an equivalence but which does not necessarily admit cofibers and fibe …
- 1,361
6
votes
0
answers
535
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Cofree conilpotent (cocommutative) coalgebra for $\infty$-categories
Let $\mathrm{K}$ be a field.
Denote $ \mathrm{Vect}_{\mathrm{K}} $ the category of K-vector spaces, $\mathrm{Coalg }^{\mathrm{conil } } $ the category of
conilpotent, coaugmented, coassociative c …
- 1,361
11
votes
2
answers
735
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When does the forgetful functor from algebras over a monad commute with homotopy geometric r...
Let $\mathcal{C}$ be a combinatorial model category and $\mathrm{T}$ a monad on
$\mathcal{C}.$
Assume that the model structure on $\mathcal{C}$ lifts to a model structure on
the category of $\math …
- 1,361
4
votes
0
answers
168
views
Building conilpotent coalgebras from co-square-zero-extensions
Let $\mathrm{K}$ be a field of char. 0.
Given a chain complex $\mathrm{X} $ over $\mathrm{K}$ denote $\mathrm{E}(\mathrm{X})$ the co-square-zero-extension on $\mathrm{X}, $ i.e. the
cocommutative no …
- 1,361
3
votes
0
answers
131
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Milnor exact sequence for homology of hopf algebras
Let $K$ be a field and $\mathrm{Hopf}^K_{E_\infty}$ the $\infty$-category of
homotopy-coherent hopf algebras over $K$ that are coherently commutative and cocommutative.
Precisely, $\mathrm{Hopf}^K_{E_ …
- 1,361
4
votes
0
answers
167
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Relation between $Tor_{C^*(BG;K)}(K,K) $ and $K^G$?
Let $K$ be an algebraically closed field and $G$ a group.
Given a dg-algebra $A$, a left $A$-module $M$ and a right $A$-module $N$
let $Tor_A(M,N)$ denote the homology of the derived tensor product $M …
- 1,361