# Tagged Questions

**1**

vote

**1**answer

152 views

### Could we extend the Atiyah class to the sheaf of poly-vector fields to get a Poisson bracket?

Let $X$ be a complex manifold and $TX$ its tangent bundle. The Atiyah class $\alpha(E)\in \text{Ext}^1(E\otimes TX, E)$ for a vector bundle $E$ is defined to be the obstruction of the global existence ...

**10**

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**4**answers

550 views

### What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class?

Let X be a complex manifold and $TX$ its tangent bundle. The Atiyah class $\alpha(E)\in \text{Ext}^1(E\otimes TX, E)$ for a vector bundle $E$ is defined to be the obstruction of the global existence ...

**5**

votes

**0**answers

151 views

### Analogue of cyclic homology for e_n-algebras?

Cyclic homology may be defined as the primitive part (with respect to a natural product) of the homology of the Lie algebra associated with the "stabilization" of an associative algebra $A$. Here the ...

**7**

votes

**3**answers

567 views

### A 2-category of chain complexes, chain maps, and chain homotopies?

First-time here... I hope my question isn't silly or anything... anyway...
Consider the category of chain complexes and chain maps. We can also define chain homotopies between chain maps. Does this ...

**0**

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**0**answers

243 views

### cokernel for $L_\infty$-algebra morphisms

As I have asked a wrong question previously, I edited a bit.
It is obvious that the cokernel construction does not work well for the category of Lie algebras. The cokernel exists only for a normal ...

**13**

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**3**answers

1k views

### Homology theory constructed in a homotopy-invariant way

Singular homology sends homotopic morphisms on equal morphisms and weakly equivalent spaces on isomorphic objects. So singular homology is in fact defined on the homotopy category of topological ...

**8**

votes

**1**answer

384 views

### Is there a “derived” Free $P$-algebra functor for an operad $P$?

Recall that an operad (in vector spaces, say) $P$ consists of a collection of vector spaces $P(n)$ for $n\geq 0$, such that $P(n)$ is equipped with an action by the symmetric group $S_n$, with maps ...

**4**

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**3**answers

476 views

### Chain Complexes and Linear Infinity-Categories

A statement I heard recently is that "chain complexes are the same thing as strict linear $\infty$-categories". Can someone explain how to see this?