Hereditarity of closure operators and injectivity

Gabriele Castellini; Eraldo Giuli

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 1, page 149-157
  • ISSN: 0010-2628

Abstract

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A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let C be a regular closure operator induced by a subcategory 𝒜 . It is shown that, if every object of 𝒜 is a subobject of an 𝒜 -object which is injective with respect to a given class of monomorphisms, then the closure operator C is hereditary with respect to that class of monomorphisms.

How to cite

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Castellini, Gabriele, and Giuli, Eraldo. "Hereditarity of closure operators and injectivity." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 149-157. <http://eudml.org/doc/247417>.

@article{Castellini1992,
abstract = {A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let $C$ be a regular closure operator induced by a subcategory $\mathcal \{A\}$. It is shown that, if every object of $\mathcal \{A\}$ is a subobject of an $\mathcal \{A\}$-object which is injective with respect to a given class of monomorphisms, then the closure operator $C$ is hereditary with respect to that class of monomorphisms.},
author = {Castellini, Gabriele, Giuli, Eraldo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {closure operator; hereditary closure operator; injective object; factorization pair; monomorphisms; codomain functor; closure operator; hereditarity; factorization pair; injectivity; idempotent hulls},
language = {eng},
number = {1},
pages = {149-157},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hereditarity of closure operators and injectivity},
url = {http://eudml.org/doc/247417},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Castellini, Gabriele
AU - Giuli, Eraldo
TI - Hereditarity of closure operators and injectivity
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 1
SP - 149
EP - 157
AB - A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let $C$ be a regular closure operator induced by a subcategory $\mathcal {A}$. It is shown that, if every object of $\mathcal {A}$ is a subobject of an $\mathcal {A}$-object which is injective with respect to a given class of monomorphisms, then the closure operator $C$ is hereditary with respect to that class of monomorphisms.
LA - eng
KW - closure operator; hereditary closure operator; injective object; factorization pair; monomorphisms; codomain functor; closure operator; hereditarity; factorization pair; injectivity; idempotent hulls
UR - http://eudml.org/doc/247417
ER -

References

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  11. Koslowski J., Closure operators with prescribed properties, Category Theory and its Applications (Louvain-la-Neuve, 1987) Springer L.N.M. 1248 (1988), 208-220. Zbl0659.18005MR0975971
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