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I've stumbled over this question, and saw that it had no answer to the "Implicit Function Theorem" part. Therefore, I wanted to address this in an answer. However, for that, I would need diagonal arrows in a commutative diagram, which seems to be not available in MSE (only through slick means such as drawing diagrams as arrays, which is quite unpleasant imho). Hence, I made the following answer in LaTeX:

http://tinyurl.com/nptoamk

and wanted to post it as an answer. This seems to be discouraged by MSE, but it seems to me that another option is unavailable. How to proceed?

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    $\begingroup$ The best thing would probably be to post the two diagrams as images, but leave the rest as plain text. $\endgroup$
    – Milo Brandt
    Nov 17 '15 at 1:45
  • $\begingroup$ @MiloBrandt Great suggestion, silly of me. That indeed takes good care of this case, and many more analogous. However, what would be the position of the community if instead of posting the diagrams as images, I posted the entire link I made as an image, for example? You see, I really don't know what is aesthetically more appealing: having an entire image, or a "fragmented" answer. $\endgroup$
    – Aloizio Macedo Mod
    Nov 17 '15 at 2:00
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Try to keep as much of your answer in text as possible; obviously, some diagrams cannot be replicated on the site and need to be posted as images and it is certainly appropriate to do so. However, these diagrams should be split off from the rest of the text so that as much as possible remains in plain text.

There's a number of reasons to do this, but the foremost is that it is possible to search text, but not possible to search images. Given that this site's purpose is to provide answers for people with questions, being searchable is very important. Other considerations are that images are harder to edit, might be less friendly to people with really slow internet connections, and probably won't work out as well on smaller screens (e.g. mobile devices).

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  • $\begingroup$ Your arguments are irrefutable. +1 and accepted. $\endgroup$
    – Aloizio Macedo Mod
    Nov 17 '15 at 2:16

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