A categorical concept of completion of objects

Guillaume C. L. Brümmer; Eraldo Giuli

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 1, page 131-147
  • ISSN: 0010-2628

Abstract

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We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.

How to cite

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Brümmer, Guillaume C. L., and Giuli, Eraldo. "A categorical concept of completion of objects." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 131-147. <http://eudml.org/doc/247368>.

@article{Brümmer1992,
abstract = {We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.},
author = {Brümmer, Guillaume C. L., Giuli, Eraldo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {firm reflection; (sub-)firm class; injective object; (co)-essential morphism; firm reflection; essential morphisms; injective objects; injective hulls; reflective subcategory},
language = {eng},
number = {1},
pages = {131-147},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A categorical concept of completion of objects},
url = {http://eudml.org/doc/247368},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Brümmer, Guillaume C. L.
AU - Giuli, Eraldo
TI - A categorical concept of completion of objects
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 1
SP - 131
EP - 147
AB - We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.
LA - eng
KW - firm reflection; (sub-)firm class; injective object; (co)-essential morphism; firm reflection; essential morphisms; injective objects; injective hulls; reflective subcategory
UR - http://eudml.org/doc/247368
ER -

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