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An example of a length 4 highest weight category which is indecompos- able and Ringel self-dual, and whose standard modules are homogeneous, is the path algebra of the linear
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
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
We consider the category ccd(set) whose objects are CCD lattices, and whose arrows are those order functions that have both, a left adjoint and a.. Proposition 5.3 gives us ii)
It is called a colax/lax adjunction, and is an instance of an orthogonal adjunction in a particular double category (in the sense recalled here in 1.3), namely the (strict)
(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
which is a Q -algebra with the continuous inverse is actually m -convex and hence entire functions operate in such a complete algebra. In the noncommutative
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
