About: Hopfian object

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In the branch of mathematics called category theory, a hopfian object is an object A such that any epimorphism of A onto A is necessarily an automorphism. The dual notion is that of a cohopfian object, which is an object B such that every monomorphism from B into B is necessarily an automorphism. The two conditions have been studied in the categories of groups, rings, modules, and topological spaces.

Attributes	Values
rdfs:label	Hopfian object (en)
rdfs:comment	In the branch of mathematics called category theory, a hopfian object is an object A such that any epimorphism of A onto A is necessarily an automorphism. The dual notion is that of a cohopfian object, which is an object B such that every monomorphism from B into B is necessarily an automorphism. The two conditions have been studied in the categories of groups, rings, modules, and topological spaces. (en)
dct:subject	Module theory Group theory Ring theory Category theory
Wikipage page ID	32290692 (xsd:integer)
Wikipage revision ID	1035956434 (xsd:integer)
Link from a Wikipage to another Wikipage	Epimorphism Module (mathematics) Monomorphism Module theory Group theory Ring theory Full linear ring Stone space Fundamental group Automorphism Category of sets Topological spaces Duality (mathematics) Field (mathematics) Finite set Projective object Ring (mathematics) Group (mathematics) Heinz Hopf Category theory ZFC Discrete space Artinian module Ascending chain condition Boolean ring Injective object Category theory Noetherian module Directly finite ring Compact manifold dbr:Finiteness_condition
Link from a Wikipage to an external page	http://ddd.uab.cat/record/62340 http://groupprops.subwiki.org/wiki/Co-Hopfian_group http://groupprops.subwiki.org/wiki/Hopfian_group
sameAs	Hopfian object Hopfian object Hopfian object
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Main
has abstract	In the branch of mathematics called category theory, a hopfian object is an object A such that any epimorphism of A onto A is necessarily an automorphism. The dual notion is that of a cohopfian object, which is an object B such that every monomorphism from B into B is necessarily an automorphism. The two conditions have been studied in the categories of groups, rings, modules, and topological spaces. The terms "hopfian" and "cohopfian" have arisen since the 1960s, and are said to be in honor of Heinz Hopf and his use of the concept of the hopfian group in his work on fundamental groups of surfaces. (en)
prov:wasDerivedFrom	wikipedia-en:Hopfian_object?oldid=1035956434&ns=0
page length (characters) of wiki page	6398 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hopfian_object
is Link from a Wikipage to another Wikipage of	Finitely generated module Heinz Hopf Co-Hopfian group Hopfian module
is Wikipage redirect of	Hopfian module
is foaf:primaryTopic of	wikipedia-en:Hopfian_object

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