I personally prefer the notation $(a_1,\ldots,a_n)$, with commas, or equivalently $(a_1\;a_2\;\ldots\;a_n)^{\mathrm{T}}$ or $[a_1\;a_2\;\ldots\;a_n]^{\mathrm{T}}$ for column vectors. And $(a_1\;a_2\;\ldots\;a_n)$ or $[a_1\;a_2\;\ldots\;a_n]$ for row vectors.

Dually, I would ask: can reading a paper that uses an obsolete mathematical language or style be even harmful for one's understanding of a theory?

What does "pigtikal" mean?

@Todd Trimble: partial answers like the one by Sergei Arbakov are ok, like answers like those in the linked questions. If you deem it should be cw, yes please go ahead and hit the button; for me, honestly, in this case it's indifferent if it's cw or not. Thank you for the attention

I'm not surprised that giving a completely general answer is nearly impossible. Still, I think some users may know the answer for many well known, occurring-in-real-life, function spaces or classes thereof.

Why do you say "the stack Isom(x,y)"? Isn't it just a sheaf of sets (over C/U)?

(Well, now that I think if it was crystallography it'd be $H^2(G,\mathbb{Z}^n)$, not $H^2(G,\mathbb{Z}/2)$)

Just out of curiosity (assuming you're a physicist as your nickname suggests): why is a physicist interested in group cohomology of abstract groups? Is it crystallography? Or discrete symmetries like "parity" and stuff like that? :)

If they ship many of these... things... I wonder what is the plural of gömböc :)

And, as Denis Nardin suggests, it should probably be $H^1(X,\mathcal{C}_{X,\mathbb{T}})$ where $\mathcal{C}_{X,\mathbb{T}}$ is the sheaf of $\mathbb{T}$-valued continuous functions on $X$, instead of $H^1(X,\mathbb{T})$.

I assume $\mathbb T =U(1)$ the circle group. From line bundles to cohomology it's: take a trivializing cover $\{U_\alpha\}$ and transition functions $\{g_{\alpha\beta}\}$; the latter represent a Cech cohomology class. From principal bundles to line bundles it's associated bundle construction $L=P\times^\mathbb{T}\mathbb{C}$. From line bundles to principal bundles it's taking the (unitary) frame bundle $L\mapsto \mathrm{Fr}^{U(1)}(L)$. From cohomology to line bundles it's: take a Cech cocycle $(\{U_\alpha\},\{g_{\alpha \beta}\}$ representative and use it as transition functions.

@Donu Arapura: presumably $U(1)$?

"I recommend reading the highly entertaining amazon review by Ian Jakovenko" - He says "Mathematicians: do NOT read this book!" though :D