Category of preordered sets information

empty set (considered as a preordered set) is the initial object of Ord, and the terminal objects are precisely the singleton preordered sets. There...

order – preorder that is antisymmetric and total Directed set Category of preordered sets Prewellordering Well-quasi-ordering For "proset", see e.g....

category of sets and maps. Let Top denote the category of topological spaces and continuous maps; and let Pro denote the category of preordered sets and monotone...

spaces Category of sets and relations Category of topological spaces Category of metric spaces Category of preordered sets Category of groups Category of abelian...

U.S. Ord, the category of preordered sets Ord, the proper class of all ordinal numbers ord(V), the order type of a well-ordered set V ordn(a), the multiplicative...

amounts to a preordered class (or a preordered set, if its objects form a set). As suggested by the name, the further requirement that the category be skeletal...

called topological sorting. Every poset (and every preordered set) may be considered as a category where, for objects x {\displaystyle x} and y , {\displaystyle...

common in a set theory are no longer possible in this framework. Equivalently, a preordered class is a thin category, that is, a category with at most...

A preordered field is a field equipped with a preordering P . {\displaystyle P.} Its non-zero elements P ∗ {\displaystyle P^{*}} form a subgroup of the...

element of a directed preordered set is a greatest element. Indeed, a directed preordered set is characterized by equality of the (possibly empty) sets of maximal...

representation categories of linear algebraic groups. A preordered monoid is a monoidal category in which for every two objects c , c ′ ∈ O b ( C ) {\displaystyle...

in an interior algebra of the form B(X) for some preordered set X giving the above-mentioned representation as a field of sets (a preorder field). This...

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general...

approximating it. Let a , b ∈ P {\displaystyle a,b\in P} be two elements of a preordered set ( P , ≲ ) {\displaystyle (P,\lesssim )} . Then we say that a {\displaystyle...

finitely many open sets (and only finitely many closed sets). A topology on a finite set can also be thought of as a sublattice of ( P ( X ) , ⊂ ) {\displaystyle...

to some element of S is necessarily also an element of S. Let ( X , ≤ ) {\displaystyle (X,\leq )} be a preordered set. An upper set in X {\displaystyle...

(X,\leq )} is a preordered set and ( X , F ) {\displaystyle (X,{\mathcal {F}})} is a field of sets. Like the topological fields of sets, preorder fields...

{\displaystyle b} of S , {\displaystyle S,} a ≤ b {\displaystyle a\leq b} (resp. a ≥ b {\displaystyle a\geq b} ). A preordered vector lattice is a preordered vector...

{\displaystyle \,\leq \,} on the set X , {\displaystyle X,} the pair ( X , ≤ ) {\displaystyle (X,\leq )} is called a preordered vector space and we say that...

contains upper bounds of finite subsets, but does not have to be a lower set. Furthermore, it is often generalized to preordered sets. A subset which is...

defined on preordered sets or classes; this article presents the common case of posets. The literature contains two closely related notions of "Galois connection"...

y'(x)=\left(x\mapsto -{\sqrt {2}}\right)'=0} . For functions between preordered sets, constant functions are both order-preserving and order-reversing;...

\varnothing } is a set and for every a ∈ A , {\displaystyle a\in A,} ( I a , ≤ ) {\displaystyle \left(I_{a},\leq \right)} is a preordered set. Then the product...