We define now a category CAT of the categories Cat[E.sub.m] which objects are categories Cat[E.sub.1], Cat[E.sub.2], ..., Cat[E.sub.m] and morphisms (functors
) are inclusion maps (canonical injections) [??] defined as:
which alleviates the functor
problem, then then the reasoner finds a quick proof in the order of 0.2 seconds.
These two results above establish a categorical equivalence between the category [[Psets.bar].sub.G] of partial actions of the group G and [[*Inj.ba.sub.G] whose objects are pairs (Q,F : Q [right arrow]* G) consisting of a groupoid and a star injective functor
from this groupoid to the group G, and whose morphisms are functors
between groupoids which entwine their respective star injective functors
to G .
Pick, "Real interpolation with logarithmic functors
," Journal of Inequalities and Applications, vol.
Vahidi, "Extension functors
of local cohomology modules," Iranian Mathematical Society Bulletin, vol.
With these Hardy inequalities, the Hardy inequalities on rearrangement-invariant Hardy space are established by using the interpolation functor
introduced in .
A quantum screen network (QS) can be defined as a Functor
from the edge screen network ES to the category of Hilbert spaces.
An involution on a category C is a contravariant functor
from C to itself of period two.
[AM10] Marcelo Aguiar and Swapneel Mahajan, Monoidal functors
, species and Hopf algebras, CRM Monograph Series, vol.
The deontic modalities themselves are proposed as values of the argument of action, thus "determining the meaning of the normative functors
with respect to the other (normative) functors
But the incorporation in (5), also might be said to "respect valency", in so far as verbs normally take functors
as complements, and among them locatives.
In 1942-45, Samuel Eilenberg (2) and Saunders Mac Lane introduced categories, functors
, and natural transformations as part of their work in topology, especially algebraic topology (see also (1), (5)).