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We didn’t have an entry direct sum of vector bundles/Whiney sum, did we? Now we do.
There is a general construction, if one takes a functor (possibly with many arguments, few covariant and few contravariant) from vector spaces to vector spaces and the functor satisfies certain continuity condition then it induces the functor on the level of vector bundles. I have covered this in my lectures last year but I think my LaTeX writeup is in Croatian. It deserves a page, though the term “continuous functor” used by classics on bundles is a bit in disconcert with terminology on the $n$Lab.
This should not be on this page. The definition is given clearly near the top, and discussion about forming pullbacks by certain constructions should go on the relevant page, for instance at pullback. It should be also stressed that conforming to house style is appreciated.
Part of “house style” has to do with section headings. We don’t have section headings that simply say “Comment”, as that is uninformative and leads to disorganized pages. A remark like this about an alternative way to express the definition (based on formal properties of pullbacks) could go at the bottom of the “Definition” section, or perhaps in the “Properties” section.
added also here the statement that the Euler class of a Whitney sum is the cup product of the separate Euler classes. Maybe I’ll copy that also over to cup product, as an example
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