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The monoidal categories determined by the quantum groups are all generalisations of the idea that the representations of a group form a monoidal category.. The corresponding
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
We call them the left double , right double and double of the monoidal.. V
Note: unital, strongly unital and subtractive categories are all pointed categories, and the morphisms 0 in the diagrams in the table represent zero morphisms in a pointed category;
(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
interests in innite loop space machines, and proves that the well known construction of a (-1)-connective spectrum out of a symmetric monoidal category is a \localization"
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
Let O be a set and V be a locally presentable cofibrantly generated monoidal simplicial model category with a monoidal fibrant replacement functor.. Then the category of V O
