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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 1st 2017

At interactions of images and pre-images with unions and intersections I have added pointer to Lawvere 69 and there at Adjointness in Foundations I added a bit more text and cross-references.

• CommentRowNumber2.
• CommentAuthorVitalyR
• CommentTimeFeb 7th 2021
Should "contained in" be removed in the explanation of the properties 2. of Proposition 2.1?
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeFeb 7th 2021

Let me see… It looks okay to me: The intersection of images may be larger than the image of the intersection.

In an extreme case, take $S_1$ and $S_2$ to two disjoint copies of the same non-empty abstract set, and each with the same image under $f$. Then the image of the intersection is empty (because the intersection itself is), but the intersection of the images is the image of either subset.

Hm, now I see that this same point is also amplified in a comment right below.

So maybe I am missing your point?

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• CommentRowNumber4.
• CommentAuthorVitalyR
• CommentTimeFeb 10th 2021
Sorry I should refer to Proposition 2.2 in the last comment. I remove "contained in" in Proposition 2.2, see the diff:
https://ncatlab.org/nlab/revision/diff/interactions+of+images+and+pre-images+with+unions+and+intersections/17

Now everything there should be OK.

I love nLab! Thanks for your great work!