Pseudo-commutative monads and pseudo-closed 2-categories

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Models of G–spectra as presheaves of spectra (2011, methodology): “quotes does not make obvious mathematical sense since there is no obvious monoidal structure on the category of symmetric monoidal categories, but category theory due to the ﬁrst author [7] (see also [14, 37]) explains what these objects are and how to rigidify them to categories enriched in permuta”
Enriched categories as a free cocompletion (2013, background): “Since Cat is cocomplete and Pκ has a rank, it follows by [16,11] that Pκ-Alg, hence also Colimκ, is a left and right closed monoidal bicategory.”
Tensor products of finitely cocomplete and abelian categories (2012, background): “The finitely cocomplete categories Rex[A,B] make the 2-category of finitely cocomplete categories, right exact functors and natural transformations into a pseudoclosed 2-category [15].”
Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures (2016, background): “Introduction Just as classical monad theory provides a general approach to study algebraic structures on objects of a category (see [5] for example), 2-dimensional monad theory offers an elegant way to investigate algebraic structures on objects of a 2-category [10, 30, 34, 37, 54, 56].”
Universality of multiplicative infinite loop space machines (2013, background): “This structure on SymMonCat has been explicitly constructed and discussed in the literature; see [14] and the more explicit [26].”