Directory UMM :Journals:Journal_of_mathematics:OTHER:
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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
If we take as D the empty doctrine, we have a duality between the 2-category of small Cauchy complete categories, functors and natural transformations, and the 2-category of
To obtain the classical examples K is CAT the 2-category of categories, T is the symmetric monoidal category monad, to say that A has a monoidal pseudo-T -algebra structure is to
We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal unit is a simple generator embeds (weakly) monoidally into the category of pre-Hilbert spaces
(iv) The homotopy category obtained from the category of small symmetric monoidal categories and strictly unital op-lax maps by inverting the weak equivalences.. (v) The
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
Given a double category with companions, one can construct a pointed equipment by using the same objects, defining the scalar arrows to be the vertical arrows of the double
The proof of May's uniqueness theorem (Ma4] Thm. 3) for functors dened from the category of permutative categories easily generalizes to show any two functors from SymMon to
