- set (considered as a
preordered set) is the
initial object of PreOrd, and the
terminal objects are
precisely the
singleton preordered sets.
There are thus...
- In mathematics, a
preordered class is a
class equipped with a preorder. When
dealing with a
class C, it is
possible to
define a
class relation on C as...
- is
canonically ****ociated to a
preordered set by
taking the open sets to be the
upper sets. Conversely, the
preordered set can be
recovered from the Alexandrov...
- {\displaystyle a,b\in P.} A
preordered class is a
class equipped with a preorder.
Every set is a
class and so
every preordered set is a
preordered class. Preorders...
-
particularly in
order theory, an
upper bound or
majorant of a
subset S of some
preordered set (K, ≤) is an
element of K that is
greater than or
equal to
every element...
-
arbitrary partially ordered sets or more generally, in
arbitrary preordered sets. For a
preordered set ( X , ≲ ) {\displaystyle (X,\lesssim )} and two elements...
- very
similar to
representation categories of
linear algebraic groups. A
preordered monoid is a
monoidal category in
which for
every two
objects c , c ′ ∈...
- {\displaystyle X,} the pair ( X , ≤ ) {\displaystyle (X,\leq )} is
called a
preordered vector space and we say that the
preorder ≤ {\displaystyle \,\leq \,}...
- {\displaystyle -1} is not in P . {\displaystyle P.} A
preordered field is a
field equipped with a
preordering P . {\displaystyle P.} Its non-zero
elements P...
- most one morphism. As such, a
posetal category amounts to a
preordered class (or a
preordered set, if its
objects form a set). As
suggested by the name...
