Monomorphisms of coalgebras

A. L. Agore. "Monomorphisms of coalgebras." Colloquium Mathematicae 120.1 (2010): 149-155. <http://eudml.org/doc/284052>.

@article{A2010,
abstract = {We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, φ: C → D is a monomorphism of coalgebras if and only if the first cohomology groups of the coalgebras C and D coincide if and only if $∑_\{i∈I\} ε(a^\{i\}) b^\{i\} = ∑_\{i∈I\} a^\{i\} ε(b^\{i\})$ for all $∑_\{i∈I\} a^\{i\}⊗ b^\{i\} ∈ C ◻_\{D\} C$. In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given.},
author = {A. L. Agore},
journal = {Colloquium Mathematicae},
keywords = {morphisms of coalgebras; monomorphisms; epimorphisms; Hopf algebras},
language = {eng},
number = {1},
pages = {149-155},
title = {Monomorphisms of coalgebras},
url = {http://eudml.org/doc/284052},
volume = {120},
year = {2010},
}

TY - JOUR
AU - A. L. Agore
TI - Monomorphisms of coalgebras
JO - Colloquium Mathematicae
PY - 2010
VL - 120
IS - 1
SP - 149
EP - 155
AB - We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, φ: C → D is a monomorphism of coalgebras if and only if the first cohomology groups of the coalgebras C and D coincide if and only if $∑_{i∈I} ε(a^{i}) b^{i} = ∑_{i∈I} a^{i} ε(b^{i})$ for all $∑_{i∈I} a^{i}⊗ b^{i} ∈ C ◻_{D} C$. In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given.
LA - eng
KW - morphisms of coalgebras; monomorphisms; epimorphisms; Hopf algebras
UR - http://eudml.org/doc/284052
ER -