About: Global element

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Global element Goto Sponge NotDistinct Permalink

An Entity of Type : dbo:ChemicalCompound, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FGlobal_element

In category theory, a global element of an object A from a category is a morphism where 1 is a terminal object of the category. Roughly speaking, global elements are a generalization of the notion of "elements" from the category of sets, and they can be used to import set-theoretic concepts into category theory. However, unlike a set, an object of a general category need not be determined by its global elements (not even up to isomorphism). For example, the terminal object of the category Grph of graph homomorphisms has one vertex and one edge, a self-loop, whence the global elements of a graph are its self-loops, conveying no information either about other kinds of edges, or about vertices having no self-loop, or about whether two self-loops share a vertex.

Attributes	Values
rdf:type	chemical compound
rdfs:label	Global element (en)
rdfs:comment	In category theory, a global element of an object A from a category is a morphism where 1 is a terminal object of the category. Roughly speaking, global elements are a generalization of the notion of "elements" from the category of sets, and they can be used to import set-theoretic concepts into category theory. However, unlike a set, an object of a general category need not be determined by its global elements (not even up to isomorphism). For example, the terminal object of the category Grph of graph homomorphisms has one vertex and one edge, a self-loop, whence the global elements of a graph are its self-loops, conveying no information either about other kinds of edges, or about vertices having no self-loop, or about whether two self-loops share a vertex. (en)
dcterms:subject	Objects (category theory)
Wikipage page ID	14717987 (xsd:integer)
Wikipage revision ID	1030266361 (xsd:integer)
Link from a Wikipage to another Wikipage	Elementary topos Graph homomorphism Morphism Clique (graph theory) Objects (category theory) Category of sets Truth value Isomorphism Subobject classifier Heyting algebra Terminal object Category (mathematics) Category theory Set theory Up to Well-pointed category Object (category theory)
sameAs	Global element Global element Global element
dbp:wikiPageUsesTemplate	dbt:Math dbt:Reflist dbt:Cattheory-stub
has abstract	In category theory, a global element of an object A from a category is a morphism where 1 is a terminal object of the category. Roughly speaking, global elements are a generalization of the notion of "elements" from the category of sets, and they can be used to import set-theoretic concepts into category theory. However, unlike a set, an object of a general category need not be determined by its global elements (not even up to isomorphism). For example, the terminal object of the category Grph of graph homomorphisms has one vertex and one edge, a self-loop, whence the global elements of a graph are its self-loops, conveying no information either about other kinds of edges, or about vertices having no self-loop, or about whether two self-loops share a vertex. In an elementary topos the global elements of the subobject classifier Ω form a Heyting algebra when ordered by inclusion of the corresponding subobjects of the terminal object. For example, Grph happens to be a topos, whose subobject classifier Ω is a two-vertex directed clique with an additional self-loop (so five edges, three of which are self-loops and hence the global elements of Ω). The internal logic of Grph is therefore based on the three-element Heyting algebra as its truth values. A well-pointed category is a category that has enough global elements to distinguish every two morphisms. That is, for each pair of distinct arrows A → B in the category, there should exist a global element whose compositions with them are different from each other. (en)
gold:hypernym	H
prov:wasDerivedFrom	wikipedia-en:Global_element?oldid=1030266361&ns=0
page length (characters) of wiki page	3225 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Global_element
is Link from a Wikipage to another Wikipage of	Timeline of category theory and related mathematics Truth value Heyting algebra Natural numbers object Well-pointed category
is foaf:primaryTopic of	wikipedia-en:Global_element

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (62 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software