# Tagged Questions

**6**

votes

**2**answers

395 views

### Homotopy Transfer Theorem for Differential Graded Associative Algebras

As in Algebra+Homotopy=Operad by Bruno Vallette, let $A$ with multiplication $\nu$ be a differential graded associative algebra equipped with degree +1 map $h$ and let $H$ be a chain complex such that ...

**2**

votes

**2**answers

366 views

### Homotopic monoids and $A_\infty$ spaces

Informally, an $A_\infty$-space is a monoid whose laws are only satisfied up to homotopy.
Letâ€™s define now what I will call a "homotopic monoid" to be a space $M$ together with a point $e\in{}M$ and ...

**6**

votes

**1**answer

267 views

### Does there exist a model of chains on oriented manifolds with both a strict intersection pairing and strict functoriality for closed embeddings?

Let $M$ be a smooth oriented $n$-dimensional manifold. My favorite model of $\operatorname{Chains}_\bullet(M) \otimes \mathbb R$ is the space of smooth compactly-supported de Rham forms on $M$, ...

**12**

votes

**4**answers

995 views

### Is an A-infinity thing the same the same as strict thing viewed through a homotopy equivalence?

If I have a topological monoid ($X,\mu$), a space $Y$ and a homotopy equivalence $f,g$ between them, then $Y$ has the structure of an $A_\infty$ space defined 'pointwise' by
$$ y_1 * y_2 := g ...

**11**

votes

**2**answers

835 views

### A-infinity tensor categories

My question is rather simple:
What is the correct notion of a monoidal A-infinity category C?
Or is there any reference where such a notion is explained?

**3**

votes

**1**answer

596 views

### $A_{\infty}$ structure of (co)homology of a space

Let $X$ be a topological space, and $Homeo(X)$ the group of self-homeomorphisms of $X$.
(1) What is the exact meaning of: $H^*(X)$ is a an $A_\infty$-module over $Homeo(X)$?
(2) Does $H_*(X)$ also ...

**19**

votes

**8**answers

2k views

### triangulated vs. dg/A-infinity

Someone recently said "derived/triangulated categories are an abomination that should struck from the earth and replaced with dg/A-infinity versions".
I have a rough idea why this is true ("don't ...

**7**

votes

**2**answers

853 views

### What's the sense in which A_\infty algebras are “deformable”?

I realise this is a very vague question! I've heard people say that A∞ algebras are the right homotopy-theoretic generalization of usual associative algebras, because you can deform them. What ...