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I added to biadjunction the statement and some references for the fact that any incoherent one can be improved to a coherent one.
Some people use “biadjoint” to refer to functor which is both left and right adjoint to . I’ve created a new page, biadjoint pair to refer to this concept, and added a notice at the top of the page warning about the ambiguity, but it may be better to replace biadjoint with a disambiguation page like bilimit.
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