Directed homotopy theory, I
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 4, pp. 281-316. 
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     author = {Grandis, Marco},
     title = {Directed homotopy theory, {I}},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {281--316},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {44},
     number = {4},
     year = {2003},
     mrnumber = {2030049},
     zbl = {1059.55009},
     language = {en},
     url = {http://archive.numdam.org/item/CTGDC_2003__44_4_281_0/}
}
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Grandis, Marco. Directed homotopy theory, I. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 4, pp. 281-316. http://archive.numdam.org/item/CTGDC_2003__44_4_281_0/

[1] F. Borceux, Handbook of categorical algebra 1-3, Cambridge University Press, Cambridge 1994. | MR | Zbl

[2] N. Bourbaki, Topologie générale, Ch. 10, Hermann, Paris 1961.

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

[4] R. Brown - P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260. | MR | Zbl

[5] E.B. Curtis, Simplicial homotopy theory, Adv. Math. 6 (1971), 107-209. | MR | Zbl

[6] L. Fajstrup - E. Goubault - M. Raussen, Algebraic topology and concurrency, Preprint 1999. | MR

[7] P. Gaucher, Homotopy invariants of higher dimensional categories and concurrency in computer science, Math. Struct. in Comp. Science 10 (2000), 481-524. | MR | Zbl

[9] P. Gaucher - E. Goubault, Topological deformation of higher dimensional automata, Preprint 2001. http://arXiv.org/abs/math.AT/0107060

[9] E. Goubault, Geometry and concurrency: a user's guide, in: Geometry and concurrency, Math. Structures Comput. Sci. 10 (2000), no. 4, pp. 411-425. | MR | Zbl

[10] M. Grandis, Cubical homotopical algebra and cochain algebras, Ann. Mat. Pura Appl. 170 (1996) 147-186. | MR | Zbl

[11] M. Grandis, Categorically algebraic foundations for homotopical algebra, Appl. Categ. Structures 5 (1997), 363-413. | MR | Zbl

[12] M. Grandis, Higher fundamental functors for simplicial sets, Cahiers Topologie Géom. Diff. Catég. 42 (2001), 101-136. | EuDML | Numdam | MR | Zbl

[13] M. Grandis, Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency, Preprint 2001. http://www.dima.unige.it/~grandis/ | MR | Zbl

[14] M. Grandis, Directed homotopy theory, II. Homotopy constructs, Dip. Mat. Univ. Genova, Preprint 446 (2001). http: / /www. dima. unige. it /-grandis / | MR | Zbl

[15] K.H. Kamps - T. Porter, Abstract homotopy and simple homotopy theory, World Scientific Publishing Co., River Edge, NJ 1997. | MR | Zbl

[16] D.M. Kan, Abstract homotopy, II, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 255-258. | MR | Zbl

[17] J.C. Kelly, Bitopological spaces, Proc. London Math. Soc. 13 (1963), 71-89. | MR | Zbl

[18] F.W. Lawvere, Metric spaces, generalized logic and closed categories, Rend-Sem. Mat. Fis. Univ. Milano 43 (1974), 135-166. | MR | Zbl

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

[20] J.P. May, Simplicial objects in algebraic topology, Van Nostrand, Princeton 1967. | MR | Zbl

[21] E. Michael, Local compactness and Cartesian products of quotient maps and k-spaces, Ann. Inst. Fourier (Grenoble) 18, 2 (1968), 281-286. | EuDML | Numdam | MR | Zbl

[22] V. Pratt, Higher dimensional automata revisited, Math. Struct. in Comp. Science 10 (2000), 525-548. | MR | Zbl

[23] D.G. Quillen, Homotopical algebra, Lecture Notes in Mathematics 43, Springer, Berlin 1967. | MR | Zbl

[24] G.W. Whitehead, Elements of homotopy theory, Springer, Berlin 1978. | MR | Zbl