cohomology

It's too dense and too focused on advanced topics (unless you're an ivy league undergrad, you don't learn cohomology).

For instance, you can interpret Maxwell equations as certain statements about de Rham cohomology classes of certain 2-forms on 4-manifolds.

It’s like rewriting a paper about sheaf cohomology in plain English without any mathematical notation and expecting it to be accessible to everyone.

Great, so what is the cohomology of the cosmos in your theory?

Sounds like you have reinvented sheaves & cohomology.

And he did it again that day, and made a bit more progress, and learned a beautiful proof for Weierstrass's theorem using the induced sheaf cohomology of the exponential sheaf sequence.

You see electromagnetism, realize that electromagnetic field is just 2-form on 4-manifold, and see that Maxwell equations just state that both this form and its Hodge dual are closed, so that they represent de Rham cohomology classes.

Well try to listen to a group theory lecture (for example on cohomology of groups) while doing chores:) But the lecture was indeed useful if you stop and rewind and see how the lecturer was explaining (there were some interesting graphs).

I admire how they build from nothing but elementary linear algebra and calculus, and end up at quite advanced topics like De Rham cohomology, of which I never imagined it had any application in computer science at all.

Categories were introduced by Eilenberg and MacLane to formalize certain structures were studying in the context of algebraic topology (homology, cohomology and homotopy are all functors from topological to algebraic categories, and there are lots of examples of natural transformations on these functors).

I find cohomology of moduli schemes thrilling too, but it is really cool when you can use a little math to solve someone's real problem, or more often, use a little math to try to dismantle something bad (see mathbabe.org for some economic applications).

At this more concrete level, then, I remember that we constructed de Rham cohomology (fixing an open subset of R^n) beginning with the cochain complex given by vector spaces of k-differential forms and exterior derivatives, instead of working more generally with a cochain complex on modules.

Why isn't there a dependency graph for the example paper "Sheaf Cohomology of Linear Predictive Coding Networks"?

Can anybody make an attempt at explaining the content of "Axiomatic Characterization of Ordinary Differential Cohomology" further than the article did?

But "they use cohomology, so they cannot be wrong".

There are literally more billionaires on HN than people in the US who could write "Axiomatic Characterization of Ordinary Differential Cohomology." Apparently some folks are motivated to strive towards those statuses.

In the preceding years people had come up with several alternative functors (Cohomology / Homology on certain topological spaces) and they needed a way to talk about in what way those constructions were equivalent to each other.