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have added a few more pointers to integrability of G-structures, in particular to the classical textbook Sternberg 64 and to the Encyclopedia-of-Mathematics entry by Alekseeviskii.
Then I wrote a section Formalization in differential cohesion.
I have been working a bit on integrability of G-structures. Gave it a decent (I hope) Idea-section and a discussion mentioning all the ingredients that go into the main Examples. Also cross-linked with all the entries mentioned there.
Added further to the Examples-section a brief paragraph on Unitary structure and added accordingly brief paragraphs to the entries that this refers to, such as Kähler manifold – In terms of G-structure and Unitary group – Relation to orthogonal, symplectic and general linear group. I suppose I also touched almost Hermitian structure and maybe other related entries.
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