Homotopy Structures for Algebras over a Monad

Applied Categorical Structures

Volumn 7, Issue 3, 1999, Pages 227-260

  Grandis, Marco ^a   Macdonald, John ^b  

^a UNIVERSITY OF GENOA   (Italy)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

(co)cylinder; Abstract homotopy; Cubical objects; Eilenberg Moore algebras; Equivariant homotopy; Fibrewise homotopy; Homotopy; Homotopy (co) limits; Monads; Slice categories

Indexed keywords

EID: 0002637231     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008678719663     Document Type: Article

References (21)

1. Baues H. J.: Algebraic Homotopy, Cambridge Univ. Press, 1989.
2. Beck J.: Distributive Laws, in Seminar on Triples and Categorical Homology Theory, Lecture Notes in Math. 80, Springer, 1969, pp. 119-140.
3. Brown R. and Higgins P. J.: On the algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260.
4. Cordier J. M. and Porter T.: Categorical aspects of equivariant homotopy, Appl. Categ. Structures 4 (1996), 195-212.
5. Crans S.: Quillen closed model structures for sheaves, J. Pure Appl. Algebra 101 (1995), 35-57.
6. Grandis M.: Homotopical algebra in homotopical categories, Appl. Categ. Structures 2 (1994), 351-406.
7. Grandis M.: Cubical monads and their symmetries, in Proceedings of the Eleventh International Conference on Topology, Trieste 1993, Rend. 1st. Mat. Univ. Trieste 25 (1993), 223-268.
8. Grandis M.: Cubical homotopical algebra and cochain algebras, Ann. Mat. Pura Appl. 170 (1996), 147-186.
9. Grandis M.: Categorically algebraic foundations for homotopical algebra, Appl. Categ. Structures 5 (1997), 363-413.
10. Grandis M.: On the homotopy structure of strongly homotopy associative algebras, J. Pure Appl. Algebra 134 (1999), 15-81.
11. Hardie K. A. and Kamps K. H.: Homotopy over B and under A, Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 183-195.
12. Hardie K. A. and Kamps K. H.: Coherent homotopy over a fixed space, in Handbook of Algebraic Topology, North-Holland, 1995, pp. 195-211.
13. James I. M.: Introduction to fibrewise homotopy, in Handbook of Algebraic Topology, North-Holland, 1995, pp. 169-194.
14. Johnstone P. T.: Adjoint lifting theorems for categories of algebras, Bull. London Mat. Soc. 1 (1975), 294-297.
15. Kamps K. H.: Kan-Bedingungen und abstrakte Homotopietheorie, Math. Z. 124 (1972), 215-236.
16. Kan D. M.: Abstract homotopy II, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 255-258.
17. Kelly G. M. and Street R.: Review of the elements of 2-categories, in Category Seminar, Sydney 1972/73, Lecture Notes in Math. 420, Springer, 1974, pp. 75-103.
18. Mac Lane S.: Categories for the Working Mathematician, Springer, 1971.
19. MacDonald J. and Stone A.: The natural number bialgebra, Cahiers Topologie Géom. Différentielle Catégoriques 30 (1989), 349-363.
20. Moerdijk I. and Svensson J. A.: Algebraic classification of equivariant homotopy 2-types, I, J. Pure Appl. Algebra 89 (1993), 187-216.
21. Stasheff J. D.: Homotopy associativity of H-spaces, II, Trans. Amer. Math. Soc. 108 (1963), 293-312.