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Added link to internal hom.
Thanks for the alert. I wasn’t aware of this entry from 2017.
It seems strange to have this classical concept discussed here in a duplicate entry under a non-clasical name with a single and non-classical reference. I wonder what the original rationale was.
Anyway, this entry should be merged with internal hom.
I have added at least a remark line at the very top of the entry, and another one above its single reference, clarifying that this entry is (unless I am missing something) a partial duplicate of internal hom.
If anyone knows what the story is with “residual” and whether there is a reason to keep this as a separate entry, please let us know.
It’s something that gets used in eg semantic models for substructural logics, which is where than Melliès–Zeilberger paper is coming from. But I agree that it shouldn’t need its own page, but a redirect and a terminology discussion at eg internal hom
There is mention of residuated lattice in relation to ideals in monoids. The link is grey, so I will create a stub entry on this. There could be perhaps additions on solving equations over idempotent semirings. I will see what I can dig up. The relations with algebras of relations, etc., may be worth chasing up with ideas about the categorification.
Thanks. If “residual” is an established term that substructural logic readers would appreciate to be reading up on, then having an entry on it makes perfect sense. But then the present entry needs to be rewritten, as currently it gives no idea that this is the case.
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