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Aspects of categorical algebra in initialstructure categories. (English) Zbl 0324.18002

MSC:
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
18Dxx Categorical structures
18A25 Functor categories, comma categories
18C10 Theories (e.g., algebraic theories), structure, and semantics
54Dxx Fairly general properties of topological spaces
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References:
[1] Antoine , P. , Extension minimale de la catégorie des espaces topologiqu es , C. R.A. S. Paris 262 ( 1966 ), 1389 - 1392 . MR 202788 | Zbl 0139.40101 · Zbl 0139.40101
[2] Baumgartner , K.H. , Categories admitting free algebras, Mimeographed Notes , Universität Bochum ( 1972 ) .
[3] Bourbaki , N. , Théorie des ensembles, Chap . 4 . Paris , Hermann ( 1970 ). MR 276101 · Zbl 0282.04001
[4] Bourdaud , G. , Foncteurs à structures initiales , Esquisses math. 8 , Paris ( 1970 ). MR 352212 | Zbl 0333.18003 · Zbl 0333.18003
[5] Brümmer , G.C.L. , A categorical study of initiality , Thesis, Kapstadt ( 1971 ). · Zbl 0218.54011
[6] Ertel , H.G. , Schubert , H. , Universelle topologische Algebra, Vorbericht , Universität Düsseldorf , April 1972 .
[7] Gray , J.W. , Fibred and cofibred categories , Proc. Conf. La Jolla 1965 , Springer , Berlin - Heidelberg - New York ( 1966 ). MR 213413 | Zbl 0192.10701 · Zbl 0192.10701
[8] Grothendieck , A. , Revêtements étales et groupe fondamental , Lecture Notes in Mathematics 224 , Springer ( 1971 ). MR 354651 · Zbl 0234.14002
[9] Herrlich , H. , Topologische Reflexionen und Coreflexionen , Lecture Notes in Mathematics 78 , Springer ( 1968 ). MR 256332 | Zbl 0182.25302 · Zbl 0182.25302
[10] Herrlich , H. , Strecker , G. , Coreflective subcategories , Trans. Amer. Math. Soc. 118 ( 1971 ), 303 - 315 . MR 280561 | Zbl 0224.18003 · Zbl 0224.18003
[11] Hoffmann , E. , Die kategorielle Aulassung der Initial- und Finaltopologie , Dissertation, Bochum ( 1972 ) .
[12] Hušek , M. , S-categories , Comm. Math. Univer. Carol. 5 ( 1964 ). MR 174027 | Zbl 0136.19101 · Zbl 0136.19101
[13] Kennison , J.F. , Reflective functors in general topology and elsewhere , Trans. Amer. Math. Soc. 118 ( 1965 ), p. 303 - 315 . MR 174611 | Zbl 0134.40705 · Zbl 0134.40705
[14] Leroux , P. , Structure et sémantique abstraites , Lecture Notes in Mathematics 195 , Springer ( 1971 ). MR 279151 | Zbl 0248.18010 · Zbl 0248.18010
[15] Roberts , J.E. , A characterization of initial functors , J. Algebra 8 ( 1968 ) 181 - 193 . MR 224674 | Zbl 0172.30904 · Zbl 0172.30904
[16] Sonner , J. , Canonical categories , Proc. Conf. La Jolla , 1965 , Springer ( 1966 ). MR 220794 | Zbl 0185.04002 · Zbl 0185.04002
[17] Pareigis , B. , Kategorien und Funktoren , Teubner , Stuttgart , 1969 . MR 265427 | Zbl 0192.34001 · Zbl 0192.34001
[18] Wischnewsky , M.B. , Algebren und Coalgebren in Initial- und Gabrielkategotien, Mimeographed Diplomarbeit , Universität München ( 1971 ).
[19] Wischnewsky , M.B. , Initialkategorien , Dissertation, Universität München ( 1972 ).
[20] Wischnewsky , M.B. , Partielle Algebren in Initialkategotien , Math. Z. 127 ( 1972 ), 83 - 91 . Article | MR 308238 | Zbl 0226.18001 · Zbl 0226.18001
[21] Wischnewsky , M.B. , Sheaves with values in initialstructure categories , Preprint München ( 1972 ) . · Zbl 0226.18001
[22] Wyler , O. , On the categories of general topology and topological algebra , Arch. d. Math. 22 / 1 ( 1971 ), 7 - 17 . MR 287563 | Zbl 0265.18008 · Zbl 0265.18008
[23] Wyler , O. , Top-categories and categorical topology , General topology and its applications 1 ( 1971 ), 17 - 28 . MR 282324 | Zbl 0215.51502 · Zbl 0215.51502
[24] Bastiani , A. , Ehresmann , C. , Categories of sketched structures , Cahiers Topo. Géo. diff. XIII- 2 ( 1972 ), 105 - 214 . Numdam | MR 323856 | Zbl 0263.18009 · Zbl 0263.18009
[25] Benabou , J. , Les distributeurs, Rapport n^\circ 33 , Université de Louvain ( 1973 ).
[26] Burroni , A. , Esquisse des catégories à limites et des quasi-topologies , Esquisses mathématiques 4 , Paris ( 1970 ). · Zbl 0395.18005
[27] Ehrig , H. , Axiomatic theory of systems and systematics , Preprint, Berlin ( 1972 ).
[28] Freyd , P.J. , Kelly , G.M. , Categories of continuous functors I , J. Pure Appl. Algebra 2 ( 1972 ), 169 - 191 . MR 322004 | Zbl 0257.18005 · Zbl 0257.18005
[29] Harting , R. , Distributoren und Kan-Erweiterungen, ETH Zürich ( 1973 ). MR 470014
[30] Gabriel , P. , Ulmer , F. , Lokal prasentierbare Kategorien , Lecture Notes in Mathematics 221 , Springer ( 1971 ). MR 327863 | Zbl 0225.18004 · Zbl 0225.18004
[31] Gabriel , P. , Zisman , M. , Calculus of fractions and homotopy theory , Springer , Berlin - Heidelberg - New York , 1967 . MR 210125 | Zbl 0186.56802 · Zbl 0186.56802
[32] Gray , J.W. , Sheaves with values in a category , Topology 3 ( 1965 ), 1 - 18 . MR 159328 | Zbl 0132.17605 · Zbl 0132.17605
[33] Kelly , G.M. , Street , R. , Abstracts of the Sydney category Seminar 1972 , The University of New South Wales , Australia, 1972 .
[34] Mac Lane , S. , Categories for the working mathematician , Springer , Berlin - Heidelberg - New york , 1972 . Zbl 0232.18001 · Zbl 0232.18001
[35] Pfender , M. , Universelle Algebra in monoidalen Kategorien , Preprint, T. U. Berlin ( 1973 ).
[36] Thiebaud , M. , Sell-dual structure-semantics and algebraic categories , Thesis, Halifax , 1971 .
[37] Wischnewsky , M.B. , Generalized universal algebra in initialstructure categories , Seminar Kasch-P areigis, Verlag Uni-Druck , München ( 1973 ). Zbl 0316.18008 · Zbl 0316.18008
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