#
Algebraically closed and existentially closed substructures in
categorical context

##
Michel Hebert

We investigate categorical versions of algebraically closed (= pure)
embeddings, existentially closed embeddings, and the like, in the context
of locally presentable categories. The definitions of S. Fakir, as well
as some of his results, are revisited and extended. Related preservation
theorems are obtained, and a new proof of the main result of Rosicky,
Adamek and Borceux, characterizing $\lambda$-injectivity classes in
locally $\lambda$-presentable
categories, is given.

Keywords:
pure morphism, algebraically closed, existentially

2000 MSC:
18A20, 18C35, 03C60, 03C40

*Theory and Applications of Categories,*
Vol. 12, 2004,
No. 9, pp 269-298.

http://www.tac.mta.ca/tac/volumes/12/9/12-09.dvi

http://www.tac.mta.ca/tac/volumes/12/9/12-09.ps

http://www.tac.mta.ca/tac/volumes/12/9/12-09.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/9/12-09.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/9/12-09.ps

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