no. 1
Categorical strong shape theory
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997) no. 1, pp. 3-66. 
@article{CTGDC_1997__38_1_3_0,
     author = {Batanin, Mikhail A.},
     title = {Categorical strong shape theory},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {3--66},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {38},
     number = {1},
     year = {1997},
     mrnumber = {1437196},
     zbl = {0873.18005},
     language = {en},
     url = {http://archive.numdam.org/item/CTGDC_1997__38_1_3_0/}
}
TY  - JOUR
AU  - Batanin, Mikhail A.
TI  - Categorical strong shape theory
JO  - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY  - 1997
SP  - 3
EP  - 66
VL  - 38
IS  - 1
PB  - Dunod éditeur, publié avec le concours du CNRS
UR  - http://archive.numdam.org/item/CTGDC_1997__38_1_3_0/
LA  - en
ID  - CTGDC_1997__38_1_3_0
ER  - 
%0 Journal Article
%A Batanin, Mikhail A.
%T Categorical strong shape theory
%J Cahiers de Topologie et Géométrie Différentielle Catégoriques
%D 1997
%P 3-66
%V 38
%N 1
%I Dunod éditeur, publié avec le concours du CNRS
%U http://archive.numdam.org/item/CTGDC_1997__38_1_3_0/
%G en
%F CTGDC_1997__38_1_3_0
Batanin, Mikhail A. Categorical strong shape theory. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997) no. 1, pp. 3-66. http://archive.numdam.org/item/CTGDC_1997__38_1_3_0/

[1] Artin M., Mazur B., On the van Kampen Theorem, Topology, 5, pp.179-189, 1966. | MR | Zbl

[2] Batanin M.A., Coherent categories with respect to monads and coherent prohomotopy theory, Cahiers Topologie et Geom. Diff., vol.XXXIV-4, pp.279-304, 1993. | Numdam | MR | Zbl

[3] Batanin M.A., Homotopy coherent category theory and A∞structures in monoidal categories, to appear. | Zbl

[4] Bauer F.W., A shape theory with singular homology, Pacific J. Math., 64, pp.25-65, 1976. | MR | Zbl

[5] Benabou J., Introduction to bicategories, in Lecture Notes in Math., vol.47, pp.1-77 Springer-Verlag, Berlin, Heidelberg, New York, 1967. | MR

[6] Benabou J., Les distributeurs, Inst. Math. Pures and Appl., Univ. Louvain-la-Neuve, Rapport No.33, 1973.

[7] Boardman J.M., R.M. Vogt, Homotopy Invariant Algebraic Structures on Topological Spaces, Lecture Notes in Math., vol. 347, Springer-Verlag, Berlin, Heidelberg, New York, 1973. | MR | Zbl

[8] Bourn D., Cordier J.-M., Distributeurs et theorie de la forme, Cahiers Topologie et Geom. Diff., 21, pp.161-189, 1980. | Numdam | MR | Zbl

[9] Bourn D., Cordier J.-M., A general formulation of homotopy limits, J.Pure Appl. Algebra, 29, pp.129-141, 1983. | MR | Zbl

[10] Bousfield A.K., Kan D.M., Homotopy Limits, Completions and Localizations, Lecture Notes in Math., vol.304, Springer-Verlag, Berlin, Heidelberg, New York, 1972. | MR | Zbl

[11] Cathey F.W., Segal J., Strong shape theory and resolutions, Topology Appl. 15, pp.119-130, 1983. | MR | Zbl

[12] Cathey F.W., Segal J., Homotopical approach to strong shape or completion theory, Topology Appl. 21, pp.167-192, 1985. | MR | Zbl

[13] Cordier J.-M., Extension de Kan simplicialement coherent, Pre-publication, Amiens, 1985.

[14] Cordier J.-M., Comparaison de deux catégories d'homotopie de morphismes cohérents, Cahiers de Topologie et Géometrie Diff. Catégoriques, vol. 30-2, pp. 257-275, 1989. | Numdam | MR | Zbl

[15] Cordier J.-M., Porter T., Vogt's Theorem on categories of homotopy coherent diagrams, Math. Proc. Cambridge Phil. Soc., vol. 100, pp 65-90, 1986. | MR | Zbl

[16] Cordier J.-M., Porter T., Shape Theory: Categorical Methods of Approximation, Ellis Horwood Limited, Chichester 1989. | MR | Zbl

[17] Cordier J.-M., Porter T., Maps between homotopy coherent diagrams, Topology and its Appl., 28, pp.255-275, 1988. | MR | Zbl

[18] Cordier J.-M., Porter T., Fibrant diagrams, rectifications and a construction of Loday, J.Pure Appl.Algebra, 67, pp.111-124, 1990. | MR | Zbl

[19] Cordier J.-M., Porter T., Homotopy coherent category theory, to appear in Transactions of the AMS, | MR | Zbl

[20] Dwyer W.G., Kan D.M., Realizing diagrams in the homotopy category by means of diagrams of simplicial sets, Proc. Amer. Math. Soc., 91, pp.456-460, 1984. | MR | Zbl

[21] Dwyer W.G., Kan D.M., Function complexes in homotopical algebra, Topology 19, pp.427-440, 1980. | MR | Zbl

[22] Dydak J., Nowak S., Strong shape for topological spaces, Transactions of the AMS, 323, n.2, pp.765-796, 1991. | MR | Zbl

[23] Edwards D.A., Hastings H.M., Čech and Steenrod Homotopy Theories with Applications to Geometric Topology, Lecture Notes in Math. 542, Springer-Verlag, Berlin, 1976. | MR | Zbl

[24] Gabriel P., Zisman M., Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, 35, Springer, 1967. | MR | Zbl

[25] Grothendieck A., Pursuing Stacks, typed manuscript, (600 pp.), 1983.

[26] Günther B., The use of semisimplicial complexes in strong shape theory, Glasnik Mat., 27, pp.101-144, 1992. | MR | Zbl

[27] Günther B., Comparison of the Coherent pro-Homotopy Theories of Edwards-Hastings, Lisica-Mardešić and Günther, Glasnik Mat., 26, pp.141-176, 1991. | MR | Zbl

[28] Heller A., Homotopy in Functor Categories, Transactions AMS., v272.272, pp.185-202, 1982. | MR | Zbl

[29] Heller A., Homotopies theories, Memoirs AMS., v.71, 383, AMS, Rhode Island, USA, 1988. | MR | Zbl

[30] Kelly G.M., The Basic Concepts of Enriched Category Theory, London Mathematical Society Lecture Notes Series, 64, (Cambridge University Press, Cambridge), 1983. | MR | Zbl

[31] Lada T.J., Strong homotopy algebras over monads, in Lecture Notes in Math., vol. 533, pp.399-479 Springer-Verlag, Berlin, Heidelberg, New York, 1976.

[32] Lisica Y.T., Mardešić S., Coherent prohomotopy and strong shape theory, Glasnik Mat., 19, pp.335-399, 1984. | MR | Zbl

[33] Maclane S., Categories for the working mathematician, Graduate Texts in Math. 5, Springer-Verlag, Berlin, Heidelberg, New York, 1971. | MR | Zbl

[34] Maclane S., Paré R., Coherence for bicategories and indexed categories, J. Pure Appl. Algebra, 37, pp.59-80, 1985. | MR | Zbl

[35] Mardešić S., Strong expansions and strong shape theory, Topology Appl., 38, pp. 275-292, 1991. | MR | Zbl

[36] Mardešić S., Segal J., Shape theory, North-Holland, Amsterdam, 1982. | MR | Zbl

[37] May J.P., The Geometry of Iterated Loop Spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, Berlin, Heidelberg, New York, 1972. | MR | Zbl

[38] Meyer J.-P., Bar and cobar constructions, J. Pure Applied Alg., 33, pp.163-207, 1984. | MR | Zbl

[39] Porter T., Stability results for topological spaces, Math. Z., 140, pp. 1-21, 1974. | MR | Zbl

[40] Porter T., On the two definitions of Ho(pro - C), Topology Appl., 28, pp. 289-293, 1988. | MR | Zbl

[41] Quillen D.G., Homotopical Algebra, Lecture Notes in Math., vol. 43, Springer-Verlag, Berlin, Heidelberg, New York, 1967. | MR | Zbl

[42] Schwänzl R., Vogt R., Homotopy homomorphisms and the Hammock localization, Boletin de la Soc. Mat. Mexicana, 37, 1-2, pp.431-449, 1992. | MR | Zbl

[43] Smirnov V.A., Homotopy theory of coalgebras, Math. USSR Izv., 27, pp.575-592, 1986. | MR | Zbl

[44] Vogt R.M., Homotopy limits and colimits, Math. Z, 134, pp.11-52, 1973. | MR | Zbl