Equilogical spaces, homology and non-commutative geometry
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 46 (2005) no. 1, pp. 53-80. 
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     title = {Equilogical spaces, homology and non-commutative geometry},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {53--80},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {46},
     number = {1},
     year = {2005},
     mrnumber = {2131961},
     zbl = {1081.18011},
     language = {en},
     url = {http://www.numdam.org/item/CTGDC_2005__46_1_53_0/}
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Grandis, Marco. Equilogical spaces, homology and non-commutative geometry. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 46 (2005) no. 1, pp. 53-80. http://www.numdam.org/item/CTGDC_2005__46_1_53_0/

[1] A. Bauer - L. Birkedal - D.S. Scott, Equilogical spaces, Theoretical Computer Science, to appear. | MR | Zbl

[2] L. Birkedal - A. Carboni - G. Rosolini - D.S. Scott, Type theory via exact categories, in: Thirteenth Annual IEEE Symposium on Logic in Computer Science (Indianapolis, IN, 1998), 188-198, IEEE Computer Soc., Los Alamitos, CA, 1998. | MR | Zbl

[3] R. Brown, Topology, Ellis Horwood, Chichester, 1988. | MR | Zbl

[4] A. Carboni - G. Rosolini, Locally cartesian closed exact completions, J. Pure Appl. Algebra 154 (2000) 103-116. | MR | Zbl

[5] A. Carboni - E. Vitale, Regular and exact completions, J. Pure Appl. Algebra 125 (1998), 79-116. | MR | Zbl

[6] A. Connes, Noncommutative geometry, Academic Press, San Diego CA 1994. | MR | Zbl

[7] A. Connes, A short survey of noncommutative geometry, J. Math. Physics 41 (2000), 3832-3866. | MR | Zbl

[8] S. Eilenberg - S. Mac Lane, Acyclic models, Amer. J. Math. 75 (1953), 189-199. | Zbl

[9] S. Eilenberg - N. Steenrod, Foundations of algebraic topology, Princeton Univ. Press 1952. | MR | Zbl

[10] M. Escardó - R. Heckmann, Topologies on spaces of continuous functions, Topology Proc. 26 No. 2, (2001-02), 545-564. | MR | Zbl

[11] M. Grandis, Homotopical algebra in homotopical categories, Appl. Categ. Structures 2 (1994), 351-406. | MR | Zbl

[12] M. Grandis, Directed combinatorial homology and noncommutative tori (The breaking of symmetries in algebraic topology), Math. Proc. Cambridge Philos. Soc., to appear. [Dip. Mat. Univ. Genova, Preprint 480 (2003).] | MR | Zbl

[13] M. Grandis, Equilogical spaces, homology and noncommutative geometry, Dip. Mat. Univ. Genova, Preprint 493 (2003).

[14] P.J. Hilton - S. Wylie, Homology theory, Cambridge Univ. Press, Cambridge 1962. | Zbl

[15] S. Mac Lane, Homology, Springer, Berlin 1963. | MR | Zbl

[16] S. Mac Lane, Categories for the working mathematician, Springer 1971. | MR | Zbl

[17] W. Massey, Singular homology theory, Springer, Berlin 1980. | MR | Zbl

[18] M. Pimsner - D. Voiculescu, Imbedding the irrational rotation C*-algebra into an AF-algebra, J. Operator Th. 4 (1980), 93-118. | MR | Zbl

[19] M.A. Rieffel, C*-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), 415-429. | MR | Zbl

[20] J. Rosický, Cartesian closed exact completions, J. Pure Appl. Algebra 142 (1999), 261-270. | MR | Zbl

[21] G. Rosolini, Equilogical spaces and filter spaces, Categorical studies in Italy (Perugia, 1997). Rend. Circ. Mat. Palermo (2) Suppl. No. 64, (2000), 157-175. | MR | Zbl

[22] D. Scott, A new category? Domains, spaces and equivalence relations, Unpublished manuscript (1996). http://www.cs. cmu. edu / Groups / LTC /

[23] R.M. Switzer, Algebraic topology - homotopy and homology, Springer, Berlin 1975. | MR | Zbl