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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
G induced by the functors that take values in finite sets inherits the monoidal structure and the resulting symmetric monoidal category also satisfies the exponential principle..
By definition, a symmetric categor- ical group is a categorification of an abelian group, and in this sense the 2-category of symmetric categorical groups SCG can be regarded as
We call them the left double , right double and double of the monoidal.. V
Here we consider a category of M¨obius intervals and construct the Hopf algebra via the objective approach applied to a monoidal extensive category of combinatorial objects, with
(For instance, this is not the case when S is the “free symmetric monoidal category” monad on categories and profunctors.) This motivates us to claim that the “right” notion
What Koslowski actually proves is that if you begin with a biclosed monoidal category there is a biclosed monoidal bicategory whose objects are the algebra objects in the
The context of enriched sheaf theory introduced in the author’s thesis provides a convenient viewpoint for models of the stable homotopy category as well as categories of finite
