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Let $(f;g)$ is a Galois connection between two posets.

Consider the special case $g\circ f = \operatorname{id}_{\operatorname{dom} f}$.

What can be said about this special case of Galois connections? Does there exist a special term for this kind of Galois connections?

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    I think its called galois insertion2012-12-17
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    Search by "A primer on Galois connections". I think you can download it for free.2012-12-17
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    @MakotoKato: Thanks but there are no word "insertion" in "A primer on Galois connections".2012-12-17
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    @porton I don't think the term "Galois insertion" is a standard one. Anyway, whatever they call it, I think the point is what can be said about it. Look for (co)reflections and interior(or closure) connections in that book.2012-12-17
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    This set of slides seems to use "Galois injection" and "Galois insertion/surjection" as different. Not sure which is which, however. See slide 21 in http://www.cs.au.dk/~jmi/AbsInt/week3.pdf2012-12-18

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