×

zbMATH — the first resource for mathematics

Semi-topological functors. I. (English) Zbl 0413.18001

MSC:
18A35 Categories admitting limits (complete categories), functors preserving limits, completions
18D30 Fibered categories
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18A22 Special properties of functors (faithful, full, etc.)
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Antoine, P., Etude élémentaire des catégories d’ensembles structurées, Bull. soc. math. belg., Bull. soc. math. belg., 18, 387-414, (1966) · Zbl 0192.10105
[2] Börger, R.; Tholen, W., Cantors diagonalprinzip für kategorien, Math. 2., 160, 135-138, (1978) · Zbl 0363.04002
[3] Brümmer, G.C.L., A categorical study of initiality in uniform topology, (1971), University of Cape Town, thesis · Zbl 0218.54011
[4] Brümmer, G.C.L., Topological functors and structure functors, (), 109-135 · Zbl 0373.18004
[5] Ehresmann, C., Catégories et structures, (1965), Dunod Paris · Zbl 0192.09803
[6] Ertel, H.-G., Topologische algebrenkategorien, Arch. math., 25, 266-275, (1974), (Basel) · Zbl 0288.18006
[7] Freyd, P.J.; Kelly, G.M., Categories of continuous functors I, J. pure appl. algebra, 2, 169-191, (1972) · Zbl 0257.18005
[8] Gabriel, P.; Ulmer, F., Lokal präsentierbare kategorien, () · Zbl 0225.18004
[9] Gray, J.W., Fibred and cofibred categories, (), 21-83 · Zbl 0192.10701
[10] Greve, G., (G, V0)-quotienten, Nordwestdeutsches kategorienseminar, (1976), Hagen
[11] Herrlich, H., Factorizations of morphisms f:B → FA, Math. Z., 114, 180-186, (1970) · Zbl 0182.34502
[12] Herrlich, H., Topological functors, General topology and appl., 4, 125-142, (1974) · Zbl 0288.54003
[13] Herrlich, H., Regular categories and regular functors, Canad. J. math., 26, 709-720, (1974) · Zbl 0255.18002
[14] Herrlich, H., Initial completions, Math. Z., 150, 101-110, (1976) · Zbl 0319.18001
[15] Hoffmann, R.-E., Die kategorielle auffassung der initial- und finaltopologie, (1972), Ruhr-Universität Bochum, thesis
[16] Hoffmann, R.-E., Semi-identifying lifts and a generalization of the duality theorem for topological functors, Math. nachr., 74, 295-307, (1976) · Zbl 0345.18002
[17] Hoffmann, R.-E., Topological functors admitting generalized Cauchy-completions, (), 286-344
[18] Hong, S.S, Categories in which every mono-source is initial, Kyungpook math. J., 15, 133-139, (1975) · Zbl 0309.18004
[19] Hong, Y.H., Studies on categories of universal topological algebras, (1974), MacMaster University Hamilton, thesis
[20] Hušek, M., Categorical methods in topology, Proc. symposium Prague 1966 on general topology, 190-194, (1967), (New York, London, Prague)
[21] MacLane, S., Categories for the working Mathematician, (1971), Springer Berlin
[22] Manes, E.G., A pullback theorem for triples in a lattice fibering with applications to algebra and analysis, Algebra univ., 2, 7-17, (1971) · Zbl 0281.46062
[23] Marny, T., Rechts-bikategoriestrukturen in topologischen kategorien, (1973), Freie Universität Berlin, thesis
[24] Pumplün, D., Universelle und spezielle probleme, Math. ann., 198, 131-146, (1972)
[25] Roberts, J.E., A characterization of topological functors, J. algebra, 8, 181-193, (1968) · Zbl 0172.30904
[26] Schubert, H., Categories, (1972), Springer Berlin
[27] Shukla, W., On top categories, () · Zbl 0278.18004
[28] Taylor, J.C., Weak families of maps, Can. math. bull., 8, 771-781, (1965) · Zbl 0137.41902
[29] Tholen, W., Relative bildzerlegungen und algebraische kategorien, (1974), Universität Münster, thesis
[30] Tholen, W., Adjungierte dreiecke, colimites und kan-erweiterungen, Math. ann., 217, 121-129, (1975) · Zbl 0325.18002
[31] Tholen, W., Factorization of cones along a functor, Quaestiones math., 2, 335-353, (1977) · Zbl 0365.18003
[32] Tholen, W., On Wyler’s taut lift theorem, General topology and appl., 8, 197-206, (1978) · Zbl 0374.18002
[33] Tholen, W., Zum satz von freyd und kelly, Math. ann., 232, 1-14, (1978) · Zbl 0351.18001
[34] Tholen, W., M-functors, Nordwestdeutsches kategorienseminar, (1976), Bremen · Zbl 0388.18005
[35] Tholen, W.; Wischnewsky, M.B., Semi-topological functors II: external characterizations, J. pure appl. algebra, 15, 75-92, (1979) · Zbl 0413.18002
[36] R. Street, W. Tholen, M.B. Wischnewsky and H. Wolff, Semi-topological functors III: Lifting of monads and adjoint functors, J. Pure Appl. Algebra (to appear). · Zbl 0428.18003
[37] Wischnewsky, M.B., Initialkategorien, (1972), Universität München, thesis · Zbl 0226.18001
[38] Wischnewsky, M.B., Partielle algebren in initialkategorien, Math. Z., 127, 83-91, (1972) · Zbl 0226.18001
[39] Wischnewsky, M.B., On the boundedness of initial-structure-categories, Manuscripta math., 12, 205-215, (1974) · Zbl 0284.18004
[40] Wyler, O., On the categories of general topology and topological algebra, Arch. math., 22, 7-17, (1971), (Basel) · Zbl 0265.18008
[41] Wyler, O., Top categories and categorical topology, General topology and appl., 1, 17-28, (1974) · Zbl 0215.51502
[42] Wyler, O., Quotient maps, General topology and appl., 3, 149-160, (1973) · Zbl 0278.54009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.