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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 12th 2012

We didn’t have an entry direct sum of vector bundles/Whiney sum, did we? Now we do.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeNov 12th 2012

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.

1. Whitney sum as pull back under diagonal map

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeDec 21st 2018

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.

2. @DavidRoberts I do not understand what is "conforming to house style".. I want to say that Whitney sum can also be seen as pullback of some bundle. It is not written in that way at the top. So, added as a comment. If you think this is definitely not suitable, please let me know, I can rollback the edit.
• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeDec 21st 2018

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.

3. I have added that at the bottom of Properties section. PLease let me know if it is ok there.
• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMar 22nd 2019

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