@Constantin-NicolaeBeli Yes, apologies, I was going to say: "If I understand correctly, you are looking for p283 of Gelfand-Manin".

arxiv.org/abs/1303.3255

This was an enormous pain when I was starting out! I suppose the most obvious thing to say is that there is no substitute for actually knowing the context around your research topic. But more practically, find someone senior in your field who writes introductions well and then read the intro to every paper they have ever written. I did this with two or three champion writers and it changed my life.

Thanks @BertramArnold; I had initially hoped that we wouldn't need to say something for all possible diagram shapes, only the C-indexed ones, but it seems that triangulated categories are much stranger than I'd initially thought.