Geodesic
Algebraically closed and existentially closed substructures in categorical context
Theory and applications of categories, Tome 12 (2004), pp. 269-298.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 18A20, 18C35, 03C60, 03C40
Keywords: pure morphism, algebraically closed, existentially 
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     author = {Michel Hebert},
     title = {Algebraically closed and existentially closed substructures in 
categorical context},
     journal = {Theory and applications of categories},
     pages = {269--298},
     publisher = {mathdoc},
     volume = {12},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2004_12_a8/}
}
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Michel Hebert. Algebraically closed and existentially closed substructures in 
categorical context. Theory and applications of categories, Tome 12 (2004), pp. 269-298. http://geodesic.mathdoc.fr/item/TAC_2004_12_a8/