Cubical homotopical algebra and cochain algebras

Annali di Matematica Pura ed Applicata

Volumn 170, Issue 1, 1996, Pages 147-186

  Grandis, Marco ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002644932     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF01758987     Document Type: Article

References (23)

1. [AL] M. AUBRY - J. M. LEMAIRE, Homotopie d'algèbres de Lie et de leurs algèbres enveloppantes, in Algebraic Topology-Rational Homotopy (Louvain-la-Neuve, 1986), pp. 26-30, Lecture Notes in Math., 1318, Springer-Verlag (1988).
2. [Ba] H. J. BAUES, Algebraic Homotopy, Cambridge Univ. Press (1989).
3. [BH1] R. BROWN - P. J. HIGGINS, On the algebra of cubes, J. Pure Appl. Algebra, 21 (1981), pp. 233-260.
4. [BH2] R. BROWN - P. J. HIGGINS, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra, 22 (1981), pp. 11-41.
5. [BH3] R. BROWN - P. J. HIGGINS, Tensor products and homotopies for u-grbupoids and crossed complexes, J. Pure Appl. Algebra, 47 (1987), pp. 1-33.
6. [Gl] M. GRANDIS, On the categorical foundations of homological and homotopical algebra, Cahiers Top. Géom. Diff. Catég., 33 (1992), pp. 135-175.
7. [G2] M. GRANDIS, Homotopical algebra in homotopical categories, Appl. Categorical Structures, 2 (1994), pp. 351-406.
8. [G3] M. GRANDIS, Cubical monads and their symmetries, in Proceedings of the Eleventh International Conference on Topology, Trieste 1993, Rend. 1st. Mat. Univ. Trieste, 25 (1993), pp. 223-262.
9. [Ka] D. M. KAN, Abstract homotopy II, Proc. Nat. Acad. Sci. U.SA, 42 (1956), pp. 255-258.
10. [KV1] M. KAROUBI - O. VILLAMAYOR, K-théorie algébrique et K-thêorie topologique, I, Math. Scand., 28 (1971), pp. 265-307.
11. [KV2] M. KAROUBI - O. VILLAMAYOR, K-théorie algébrique et K-théorie topologique, H, Math. Scand., 32 (1973), pp. 57-86.
12. [Km1] K H. KAMPS, Faserungen and Cofaserungen in Kategorien mit Homotopiesystem, Dissertation (Saarbrücken 1968), pp. 1-142.
13. [Km2] K H. KAMPS, Über einige formale Eigenschaften von Faserungen und h-Faserungen, Manuscripta Math., 3 (1970), pp. 237-255.
14. [Km3] K H. KAMPS, Kan-Bedingungen und abstrakte Homotopietheorie, Math. Z., 124 (1972), pp. 215-236.
15. [M1] H. J. MUNKHOLM, The Eilenberg-Moore spectral sequence and strongly homotopy commutative maps, J. Pure Appl. Algebra, 5 (1974), pp. 1-50.
16. [M2] H. J. MUNKHOLM, Shm maps of differential algebras, I. A characterization up to homotopy, J. Pure Appl. Algebra, 9 (1976-77), pp. 39-46.
17. [M3] H. J. MUNKHOLM, Shm maps of differential algebras, II. Applications to spaces with polynomial cohomology, J. Pure Appl. Algebras, 9 (1976-77), pp. 47-63.
18. [M4] H. J. MUNKHOLM, DGA algebra as a Quillen model category. Relations to shm maps, J. Pure Appl. Algebra, 13 (1978), pp. 221-232.
19. [N1] S. NIEFIELD, Cartesianness: topological spaces, uniform spaces, and affine schemes, J. Pure Appl. Algebra, 23 (1982), pp. 147-167.
20. [N2] S. NIEFIELD, Adjoints to tensor for graded algebras and coalgebras, J. Pure Appl. Algebra, 41 (1986), pp. 155-161.
21. [Pu] D. PUPPE, Homotopiemengen und ihre induzierten Abbildungen, I, Math. Z, 69 (1958), pp. 299-344.
22. [Q1] D. G. QUILLEN, Homotopical algebra, Led. Notes in Math., 43, Springer-Verlag (1967).
23. [Rd] S. RODRIGUEZ, Homotopta en categorias aditivas, Rev. Acad. Cienc. Zaragoza, 43 (1988), pp. 77-92.