@inbook{e7585fa4bb644e81b975c579368969d1,

title = "Monoidal functors generated by adjunctions, with applications to transport of structure",

abstract = "B{\' }enabou pointed out in 1963 that a pair f ⊣ u : A → B of adjoint functors induces a monoidal functor [f, u] : [A, A] → [B, B] between the (strict) monoidal categories of endofunctors. We show that this result about adjunctions in the monoidal 2-category Cat extends to adjunctions in any right-closed monoidal 2-category V, or more gen- erally in any 2-category A with an action ∗ of a monoidal 2-category V admitting an adjunction A(T ∗ A, B) ∼= V(T, ⟨A, B⟩); certainly such an adjunction exists when ∗ is the canonical action of [A, A] on A, pro- vided that A is complete and locally small. This result allows a concise and general treatment of the transport of algebraic structure along an equivalence.",

author = "Stephen Lack",

year = "2004",

language = "English",

isbn = "9780821832905 ",

series = "Fields Institute Communications",

publisher = "American Mathematical Society",

pages = "319--340",

editor = "Janelidze, {George } and Pareigis, {Bodo } and Tholen, {Walter }",

booktitle = "Galois theory, Hopf algebras, and semiabelian categories",

address = "United States",

}