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With the evident compositions there is a 2-category BrOpMon whose objects are braided monoidal categories, whose arrows are braided opmonoidal functors and whose 2-cells are
gory object within the category of symmetric pre-cubical categories and symmetric cubical functors, as made explicit in the preceding section, which is further equipped with
We define the notion of an additive model category and prove that any stable, additive, combinatorial model category M has a model enrichment over Sp Σ (sAb) (symmetric spectra based
of naturally Mal’tsev and essentially affine categories coincide with the notion of finitely complete additive category.. There is a well known intermediate notion, namely
The notion of a differential category provides a basic axiomatization for differential operators in monoidal categories, which not only generalizes the work of Ehrhard and Regnier
A Gray-monoid [DS97, Section 1] may be considered to be a monoidal2-category, and in fact every monoidal 2-category is biequivalent to a Gray-monoid [GPS95, Section 8.1]; indeed this
Our two questions about the behavior of projective objects in symmetric monoidal closed abelian categories fit naturally into a larger group of six interrelated questions about
To give a 2-monad on a locally-discrete 2-category is just to give a monad on the corresponding category; and thus all that has gone before can be applied to ordinary monads
