Geodesic
Total Categories and Solid Functors
Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 213-229

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

Totality of a category as introduced by Street and Walters [17] is known to be a strong cocompleteness property (cf. also [21]) which goes far beyond ordinary (small) cocompleteness. It implies compactness in the sense of Isbell [11] and therefore hypercompleteness [7], that is: the existence of limits of all those (not necessarily small) diagrams which are not prevented from having a limit merely from size-considerations with respect to the homsets. In particular, arbitrary intersections of monomorphisms exist in a total category; which is part of Street's [16] characterization of totality and is used in establishing the interrelationship with topoi (cf. also [15]). 
Börger, Reinhard; Tholen, Walter. Total Categories and Solid Functors. Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 213-229. doi: 10.4153/CJM-1990-012-x
@article{10_4153_CJM_1990_012_x,
     author = {B\"orger, Reinhard and Tholen, Walter},
     title = {Total {Categories} and {Solid} {Functors}},
     journal = {Canadian journal of mathematics},
     pages = {213--229},
     year = {1990},
     volume = {42},
     number = {2},
     doi = {10.4153/CJM-1990-012-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1990-012-x/}
}
TY  - JOUR
AU  - Börger, Reinhard
AU  - Tholen, Walter
TI  - Total Categories and Solid Functors
JO  - Canadian journal of mathematics
PY  - 1990
SP  - 213
EP  - 229
VL  - 42
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1990-012-x/
DO  - 10.4153/CJM-1990-012-x
ID  - 10_4153_CJM_1990_012_x
ER  - 
%0 Journal Article
%A Börger, Reinhard
%A Tholen, Walter
%T Total Categories and Solid Functors
%J Canadian journal of mathematics
%D 1990
%P 213-229
%V 42
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1990-012-x/
%R 10.4153/CJM-1990-012-x
%F 10_4153_CJM_1990_012_x

[1] 1. Adámek, J., Colimits of algebras revisited, Bull. Austral. Math. Soc. 17 (1977), 433–450. Google Scholar

[2] 2. Adámek, J., How complete are categories in algebras? Bull. Austral. Math. Soc. 36 (1987), 389-09. Google Scholar

[3] 3. Anghel, C., Factorizations and initiality in enriched categories, Doctoral dissertation, Fernuniversität Hagen (1987). Google Scholar

[4] 4. Anghel, C., Lifting properties of V-functors, preprint (1987). Google Scholar

[5] 5. Börger, R. and Tholen, W., Cantors Diagonalprinzip für Kategorien, Math. Z. 160 (1978), 135- 138. Google Scholar

[6] 6. Börger, R. and Tholen, W., Strong, regular, and dense generators, Cahiers Topologie Géom. Différentielle Catégoriques (submitted). Google Scholar

[7] 7. Börger, R., Tholen, W., Wischenwsky, M.B. and Wolff, H., Compact and hypercomplete categories, J. Pure Appl. Algebra 21 (1981), 120-144. Google Scholar

[8] 8. Day, B.J., Further criteria for totality, Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 77–78. Google Scholar

[9] 9. Gabriel, R and Ulmer, F., Lokalpräsentierbare Kategorien, Lecture Notes in Math. 221 (Springer- Verlag, Berlin-Heidelberg-New York, 1971). Google Scholar

[10] 10. Hoffmann, R.-E., Topological functors admitting generalized Cauchy-completion, Lecture Notes in Math. 540 (Springer-Verlag, Berlin-Heidelberg-New York, 1976) 286–344. Google Scholar

[11] 11. Isbell, J.R., Small subcategories and completeness, Math. Systems Theory 2 (1968), 27–50. Google Scholar

[12] 12. Kelly, G.M., A survey of totality for enriched and ordinary categories, Cahiers Topologie Géom. Différentielle Catégoriques 27 (1986), 109–131. Google Scholar

[13] 13. Mac Lane, S., Categories for the working mathematician (Springer-Verlag, Berlin-Heidelberg- New York, 1971). Google Scholar

[14] 14. Pareigis, B., Categories and functors (Academic Press, New York-London, 1970). Google Scholar

[15] 15. Street, R., Notions of topos, Bull. Austral. Math. Soc. 23 (1981), 199–208. Google Scholar

[16] 16. Street, R., The family approach to total cocompleteness and toposes, Trans. Amer. Math. Soc. 284 (1984), 355–369. Google Scholar

[17] 17. Street, R. and Walters, R., Yoneda structures on 2-categories, J. Algebra 50 (1978), 350–379. Google Scholar

[18] 18. Tholen, W., Semi-topological functors I, J. Pure Appl. Algebra 15 (1979), 53–73. Google Scholar

[19] 19. Tholen, W., Note on total categories, Bull. Austral. Math. Soc. 21 (1980), 169–173. Google Scholar

[20] 20. Tholen, W., Factorizations, localizations and the orthogonal subcategory. Google Scholar

[21] 21. Wood, R.J., Some remarks on total categories, J. Algebra 75 (1982), 538–545. Google Scholar

Cité par Sources :