On pure quotients and pure subobjects

Jiří Adámek; Jiří Rosický

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 3, page 623-636
  • ISSN: 0011-4642

Abstract

top
In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.

How to cite

top

Adámek, Jiří, and Rosický, Jiří. "On pure quotients and pure subobjects." Czechoslovak Mathematical Journal 54.3 (2004): 623-636. <http://eudml.org/doc/30887>.

@article{Adámek2004,
abstract = {In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.},
author = {Adámek, Jiří, Rosický, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {pure quotient; pure subobject; locally presentable category; semi-abelian category; abelian category; pure quotient; pure subobject; locally presentable category; semi-abelian category; abelian category},
language = {eng},
number = {3},
pages = {623-636},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On pure quotients and pure subobjects},
url = {http://eudml.org/doc/30887},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Adámek, Jiří
AU - Rosický, Jiří
TI - On pure quotients and pure subobjects
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 623
EP - 636
AB - In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.
LA - eng
KW - pure quotient; pure subobject; locally presentable category; semi-abelian category; abelian category; pure quotient; pure subobject; locally presentable category; semi-abelian category; abelian category
UR - http://eudml.org/doc/30887
ER -

References

top
  1. Locally Presentable and Accessible Categories, Cambridge Univ. Press, Cambridge, 1994. (1994) MR1294136
  2. 10.1006/jabr.1999.8249, J.  Algebra 228 (2000), 143–164. (2000) Zbl0969.18008MR1760960DOI10.1006/jabr.1999.8249
  3. Objects algébraiquement clos et injectifs dans les catégories localement présentables, Bull. Soc. Math. France 42 (1975). (1975) MR0401879
  4. Semi-abelian categories, 168 (2002), 367–386. (2002) MR1887164
  5. Catégories modélables et catégories esquissables, Diagrammes (1981), 1–20. (1981) Zbl0522.18008MR0684749
  6. 10.1090/conm/104, Contemp. Math. Vol. 104, Amer. Math. Soc., Providence, 1989. (1989) MR1031717DOI10.1090/conm/104
  7. Purity in model theory, In: Advances in Algebra and Model Theory, M.  Droste and R.  Göbel (eds.), Gordon and Breach, , 1997, pp. 445–469. (1997) Zbl0931.03055MR1687736

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.