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In case when V is the category Ab of Abelian groups and their homomorphisms, connected functors between one-object categories (that is, homomorphisms of rings with unit) 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..
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
Our central observation is that model categories are the objects of a double category whose vertical and horizontal ar- rows are left and right Quillen functors, respectively, and
As a by-product we get the classification of locally con- stant sheaves with values in finite categories (e.g. in the category defined by a group) which yields an amusing way to
In [CKW] the theory was illustrated in detail with a section devoted to rel seen as a colax functor from the 2-category REG of regular categories, arbitrary functors, and
If Φ is a small class of weights we can define, as we did for J -Colim, a2-category Φ- Colim of small categories with chosen Φ-colimits, functors preserving these strictly, and
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