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Adjointness in foundations. (English) Zbl 0341.18002

MSC:
18A15 Foundations, relations to logic and deductive systems
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18C10 Theories (e.g., algebraic theories), structure, and semantics
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
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