A new diagram about funcoids and reloids

Define for posets with order Image may be NSFW.
Clik here to view.:

1. Image may be NSFW.
   Clik here to view.;
2. Image may be NSFW.
   Clik here to view..

Note that the above is a generalization of monotone Galois connections (with Image may be NSFW.
Clik here to view. and Image may be NSFW.
Clik here to view. replaced with suprema and infima).

Then we get the following diagram (see this PDF file for a proof):

Image may be NSFW.
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It is yet unknown what will happen if we keep apply Image may be NSFW.
Clik here to view. and/or Image may be NSFW.
Clik here to view. to the node “other”. Will this lead to a finite or infinite set?