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Adj' in Adj, Back to Beck

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The adjoints given by Beck’s monadicity theorem come with associated 2-cells. The viewpoint also applies to a general adjoint lifting problem.


  1. Beck, 1967, Triples, algebras and cohomology, Theorem 1 (1).
  2. Dubuc, 1968, Adjoint Triangles, Lecture Notes in Mathematics 61, Theorem 1.
  3. Power, 1988, A Unified Approach to the Lifting of Adjoints, Lemma 2.2.

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