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Simplicial algebroids and internal categories within \(R\)-algebroids. (English) Zbl 1442.18012
Summary: In this work, by defining Peiffer pairings in the Moore complex of a simplicial algebroid, we give the close relationship between the category of simplicial algebroids with Moore complex of length 1 and that of internal categories in the category of \(R\)-algebroids.
18C40 Structured objects in a category (group objects, etc.)
18N40 Homotopical algebra, Quillen model categories, derivators
18N50 Simplicial sets, simplicial objects
18G50 Nonabelian homological algebra (category-theoretic aspects)
Full Text: DOI Euclid
[1] Z. Arvasi and T. Porter, Higher dimensional Peiffer elements in simplicial commutative algebras. Theory and Applications of Categories Vol.3, No 1,(1997) pp.1-23. · Zbl 0874.18011
[2] Z. Arvasi and T. Porter, Freeness conditions for 2-crossed module of commutative algebras, Applied Categorical Structures, 6,(1998) 455-477. · Zbl 0923.18003
[3] R. Brown, and J. L.Loday, van Kampen theorems for diagrams of spaces, Topology, Vol. 26, No. 3, (1987) 311-335. · Zbl 0622.55009
[4] R. Brown and C. B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Konn. Ned. Akad. v. Wet. 79,(1976) 296-302. · Zbl 0333.55011
[5] D. Conduché, Modules croisés généralisés de longueur 2, Journal Pure Appl. Algebra, 34, (1984) 155-178. · Zbl 0554.20014
[6] J. Duskin, Simplicials Methods and the Interpretation of Triple cohomology, Memoirs A.M.S. Vol.3 163, (1975) · Zbl 0376.18011
[7] B. Mitchell, Rings with several objects, Advances in Mathematics 8(1)(1972) 1-161. · Zbl 0232.18009
[8] B. Mitchell, Some applications of module theory to functor categories, Bull. Amer. Math. Soc. 84,(1978) 867- 885. · Zbl 0389.18005
[9] G. H. Mosa, Higher dimensional algebroids and crossed complexes, PhD Thesis, University College of NorthWales, Bangor, (1986).
[10] T. Porter, Homology of Commutative Algebras and an Invariant of Simis and Vasconceles J. Algebra 99,(1986) 458-465. · Zbl 0594.13011
[11] J. H. C. Whitehead, Combinatorial Homotopy I and II, Bull. Amer. Math. Soc. 55 (1949), 231-245 and 453-496. · Zbl 0040.38704
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