Geodesic
Normal Completions of Small Categories
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 196-201

Voir la notice de l'article provenant de la source Cambridge University Press

In (3), Isbell proposed a stronger definition for the term “complete category” and obtained many nice theorems for the resulting notion of a completion. In particular, he showed (3, Theorem 3.20) that completions of small categories satisfy a strong normality condition.In this paper we shall always use the term “complete” in the weaker sense of Freyd (1). (In (3), Isbell used the term “small-complete” for this weaker notion.) We shall prove that the completions, in the sense of Freyd, of small categories also enjoy the same normality condition, provided they admit at least one bicategory structure. (The complete categories in the sense of Isbell always admit bicategory structures; see the remark following Proposition 2.4.)In what follows, we let mean that is a full subcategory of . Moreover, if , then means that each object of is equivalent to an object in . 
Kennison, J. F. Normal Completions of Small Categories. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 196-201. doi: 10.4153/CJM-1969-019-6
@article{10_4153_CJM_1969_019_6,
     author = {Kennison, J. F.},
     title = {Normal {Completions} of {Small} {Categories}},
     journal = {Canadian journal of mathematics},
     pages = {196--201},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-019-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-019-6/}
}
TY  - JOUR
AU  - Kennison, J. F.
TI  - Normal Completions of Small Categories
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 196
EP  - 201
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-019-6/
DO  - 10.4153/CJM-1969-019-6
ID  - 10_4153_CJM_1969_019_6
ER  - 
%0 Journal Article
%A Kennison, J. F.
%T Normal Completions of Small Categories
%J Canadian journal of mathematics
%D 1969
%P 196-201
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-019-6/
%R 10.4153/CJM-1969-019-6
%F 10_4153_CJM_1969_019_6

[1] 1. Freyd, P., Abelian categories (Harper and Row, New York, 1964). Google Scholar

[2] 2. Isbell, J. R., Some remarks concerning categories and subspaces, Can. J. Math. 9 (1957), 563–577. Google Scholar

[3] 3. Isbell, J. R., Structure of categories, Bull. Amer. Math. Soc. 72 (1966), 619–655. Google Scholar

[4] 4. Isbell, J. R., Subobjects, adequacy, completeness and categories of algebras, Rozprawy Mat. 34 (1964), 1–33. Google Scholar

[5] 5. Kennison, J. F., A note on reflection mappings, Illinois J. Math. 11 (1967), 404–409. Google Scholar

[6] 6. Lambek, J., Completions of categories, Lecture Notes in Mathematics, Vol. 24 (Springer- Verlag, Berlin, 1966). Google Scholar

Cité par Sources :