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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..
The tree monad T on Glob (the category of globular sets) described in section (9) is cartesian and, as pointed out in [Lei00], a T -operad is an operad in the monoidal globular
Summing up, to model intuitionistic linear logic we need a symmetric monoidal closed category, with finite products and coproducts, equipped with a linear exponential comonad.. To
In order to extend this functor to a strict monoidal 2-functor we need a compatible selection of 2-cells satisfying the conditions of Lemma 5.6.. Let us call this
A bit more 2-category theory than we have discussed here (see [Kel74]) gives us a notion of ‘lax/oplax’ framed adjunction, in which the left adjoint is oplax and the right adjoint
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
(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
