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A fully extended tqft is not quite a generalized homology theory... But almost. You can find a preliminary reference here (notes of a talk by Hiro Tannaka at the mit Talbot workshop): http://math.mit …

Have you looked at Joachim Kock's book "Frobenius algebras and 2D topological quantum field theories"?

First of all remember that differentiating the action of $G$ at the identity gives you a Lie algebra morphism $\mathfrak{g}\to\Gamma(T_X)$, and thus, for any point $x\in X$, a map $\mathfrak g\to T_xX …

Hi Kevin, even if the question is answered I would like to add a few remarks. (0) the claim that this quasi-isomorphism $U$ is compatible with the dg algebra structures on $T$ and $D$ is …

In addition to the references pointed out by Stefan, I would like to add Déformation, quantification, et théorie de Lie, by Catteno, Keller, and Torossian (Part I and Part III are actually in Engl …

Here is a concrete example of a one week reading seminar that was organized on derived algebraic geometry: https://video.ethz.ch/events/2013/dag.html

I believe the thesis of Kenji Lefèvre-Hasegawa is a remarkable piece of work, and is very readable (references spotted by Samuel Tinguely are very good, but they are about $A_\infty$-algebras): https: …

Récoltes et semailles, by Alexander Grothendieck (available at the Grothendieck circle), might be considered as an autobiography.

I would recommend the work of Adiprasito, Huh and Katz: K. Adiprasito, J. Huh, E. Katz, Hodge Theory for Combinatorial Geometries, Annals of Mathematics 188 (2018), 381–452. [arXiv]. [Journal] They …

This is a long comment, rather than an answer. As far as I understand, on the one hand we have the Lie algebra appearing in the paper of Connes and Dubois-Violette, that is the graded Lie algebra $\ma …

I might be wrong but it seems to me that the $p$-th Atiyah class does not have any reason to agree with the usual $p$-th Chern class unless the manifold under consideration is Kahler. Namely, if $X$ …

It is definitely not known if $\zeta(3)/\pi^3$ is rational or not. By the way, there is a paper of Felder and Willwacher where they prove that the weight of a certain graph appearing in Kontsevich's f …

Well. Even in the case of a DG (or $A_\infty$) algebra $A$, infinitesimal (i.e. 1st order) deformations are classified by $HH^2(A,A)$. Namely, the structure maps (a-k-a Taylor components) of an $A_\in …

Disclaimer: this is not an answer to the question as I have no explanation for why people don't introduce natural transformations in the way explained in the question, but I am posting this in order t …

$A_n$-spaces are already discussed in the original paper of Stasheff, Homotopy associativity of H-spaces, I and II. In the linear setting, $A_n$-algebras are discussed e.g. in A∞-algebras, spectral se …