For more references, see the references in the (revised)
[45].
Some publications in non-abelian homological and homotopical algebra
This Bibliography lists some papers and books on multiple categories and
groupoids, non-linear homological algebra, and related areas directly relevant
to the themes developed in the accompanying article on
Higher dimensional group theory.
This bibliography should be related to papers on Lie groupoids, Lie algebroids
and Lie pseudoalgebras in a
bibliography
compiled by Kirill Mackenzie.
Papers added in 2004 are coloured brown.
September 25, 2008 The subject is advancing so much that it is not
possible for me to keep this list up to date. See also the
n-category cafe.
R.Aboughazi, `Produit tensoriel du groupe d'Heisenberg', Bull. Soc. Math.
France, 15, 95-106, 1987.
G. Abramson, J.-P.Meyer, J.Smith, `A higher dimensional analogue of the
fundamental groupoid', in Recent developments of algebraic topology, RIMS
Kokyuroku 781, Kyoto, 38-45, 1992.
F.Al-Agl, Aspects of multiple categories, University of Wales PhD Thesis,
1989.
F.Al-Agl and R.J.Steiner, `Nerves of multiple categories', Proc. London Math.
Soc., 66, 92-128, 1992.
F.Al-Agl, R. Brown and R.J.Steiner,
`Multiple categories: the equivalence between a globular
and cubical approach', Advances in Mathematics, 170 (2002)
71-118. pdf
M. Alp and C.D. Wensley, Enumeration of cat1-groups of low order
(97.05),
IJAC (to appear).
Z. Arvasi and T. Porter, Simplicial and Crossed Resolutions of Commutative
Algebras, J Algebra, 181, 1996, 426-448.
Z. Arvasi and T. Porter, Higher dimensional Peiffer elements in Simplicial
Commutative Algebras, Theory and Applications of Categories, 3 (1997) 1-23.
N.Ashley, Simplicial T-complexes, University of
Wales PhD Thesis, 1976, published as Simplicial T-complexes: a non-abelian
version of a theorem of Dold-Kan, Diss. Math. 165, 11-58 (1988).
M.F. Atiyah, `Mathematics in the
20th century', Bulletin London Math. Soc. 34 (2002) 1-15.
M.R.Bacon, `On the non-abelian square of a nilpotent group of class 2', Glasgow
Math. J. 36 (1994) 291-297.
M.R.Bacon, L.-C. Kappe, `The non-abelian square of a 2-generator $p$-group
of class 2', Arch. math., 61 (1993) 508-516.
J. C. Baez, J.Dolan, `Higher-dimensional algebra and
topological quantum field theory', Jour. Mat. Physics 36 (1995) 6073-6105.
J. Baez and M. Neuchl, `Higher dimensional algebra I: Braided monoidal
2-categories', Adv. Math. 121 (1996) 196-244.
J. C. Baez, J.Dolan, `Higher-dimensional algebra III: n-categories
and the algebra of Opetopes', Riverside Preprint, February, 1997.
Y.-G. Baik, J.Howie, S.J.Pride, `The identity problem for graph products
of groups', J. Algebra 162 (1993) 168-177.
I. C. Baianu, R. Brown, G. Georgescu, and J. F.
Glazebrook, `Complex nonlinear biodynamics in categories: higher dimensional
algebra, and Lukasiewicz--Moisil Topos: transformations of neuronal, genetic
and neoplastic networks', Axiomathes (to appear) 57 pages. UWB Preprint 05.13
J.Barja, C.Rodriguez, `Homology groups and eight term exact sequences', Cah.
Top. Géom. Diff. Cat. 31, 91-120, 1990.
H.J.Baues, Algebraic homotopy, Cambridge University Press, 1989.
H.J.Baues, Combinatorial homotopy and 4-dimensional complexes, De
Gruyter, 1991.
H.J.Baues, `Homotopy types', in Handbook of algebraic
topology, ed. I. M. James, 1995, 78 pp.
H.J.Baues, D.Conduché, `The central series for Peiffer commutators
in groups with operators', J.Algebra, 133, 1-34, 1990.
H.J.Baues, D.Conduché, `The tensor algebra
of a non-Abelian group', K-theory, 5, 531-554, 1992.
H.J.Baues, R.Brown, `On the relative homotopy groups
of the product filtration and a formula of Hopf', J. Pure Appl. Algebra 89,
49-61, 1993.
H. J. Baues, A. Tonks, `On the twisted cobar construction',
Math. Proc. Camb. Phil. Soc., 121 (1997) 229-245.
W.A.Bogley, M.A.Gutierrez, `Mayer-Vietoris sequences in homotopy of 2-complexes
and in homology of groups', J. Pure Appl. Algebra 77, 39-65, 1992.
R. Brown, Topology: a geometric account of general
topology, homotopy types and the fundamental groupoid, Ellis Horwood,
Chichester, (1988) (first edition, McGraw Hill, 1968). Republished privately
as `Topology and Groupoids' Booksurge, 2006.
R.Brown, `On the second relative homotopy group of an
adjunction space: an exposition of a theorem of J.H.C.Whitehead', J. London
Math. Soc. (2) 22, 146-152, 1980.
R. Brown, `Non-abelian cohomology and the homotopy
classification of maps' , in Homotopie alg\'ebrique et algebre locale,
Conf. Marseille-Luminy 1982, ed. J.-M. Lemaire et J.-C. Thomas, Ast\'erisques
113-114 (1984), 167-172.
R.Brown, `From groups to groupoids: a brief survey',
Bull. London Math. Soc., 19, 113-134, 1987.
pdf
R.Brown, Elements of Modern Topology, McGraw Hill, Maidenhead, 1968; Topology:
a geometric account of general topology, homotopy types and the fundamental
groupoid, Ellis Horwood, Chichester, 1988. new
edition
R.Brown, `Triadic Van Kampen theorems and Hurewicz theorems', Proc. Int.
Conf. Algebraic Topology, Evanston, 1988 ed. M.Mahowald, Cont. Math. 96,
113-134, 1989.
R.Brown, `Some problems in non-Abelian homological and homotopical algebra',
Homotopy theory and related topics: Proceedings Kinosaki, 1988, Edited
M.Mimura, Springer Lecture Notes in Math. 1418, 105-129, 1990.
pdf
R.Brown, `$q$-perfect groups and universal $q$-central extensions', Publicacions
Mat. 34, 291-297, 1991.
R.Brown, `Computing homotopy types using crossed
$n$-cubes of groups', Proc. Adams Memorial Symposium on Algebraic Topology,
Manchester 1990, Volume I, ed N.Ray and G. Walker, London Math. Soc. Lecture
Note Series 175, Cambridge University Press, 187-210, 1991.
pdf
R.Brown, `Homotopy theory, and change of base for groupoids and multiple
groupoids', Applied Categorical Structures 4 (1996) 175-193.
pdf
R. Brown, `Representation and computation for crossed modules', Proceedings
Catégories, Algebres, Esquisses, Neo-esquisses, Caen, 1994,
6pp.
R. Brown, `Crossed complexes and homotopy groupoids
as non commutative tools for higher dimensional local-to-global problems',
Proceedings of the Institute Workshop on Categorical Structures for Descent
and Galois Theory, Hopf Algebras and Semiabelian Categories, September 23-28,
Fields Institute Communications 43 (2004) 101-130. UWB
Math Preprint 02.26 (30 pp).
pdf
R. Brown, M. Dyer, `The homotopy classification of maps of crossed complexes',
(in preparation).
R. Brown and G. J. Ellis, `Hopf formulae for the higher
homology of a group', Bull. London Math. Soc., 20 (1988) 124-128.
erratum
R.Brown, N.D.Gilbert, `Algebraic models of 3-types
and automorphism structures for crossed modules', Proc. London Math. Soc.
(3) 59, 51-73, 1989. pdf
R.Brown, M.Golasinski, `A model structure for the homotopy theory of crossed
complexes', Cah. Top. Géom. Diff. Cat. 31, 61-82, 1989.
pdf
R.Brown, M.Golasinski, T. Porter, A. Tonks, `Spaces of maps into classifying
spaces for equivariant crossed complexes', Indag. Math. 8 (1977) 157-172.
R.Brown, M.Golasinski, T. Porter, A. Tonks, `Spaces of maps into classifying
spaces for equivariant crossed complexes II: The general topological group
case',
Preprint
number 98.15. 29pp. K-Theory 23 (2001)129-155.
R.Brown, P.J.Higgins, `On the connection between the
second relative homotopy groups of some related spaces', Proc. London Math.
Soc. (3), 36, 193-212, 1978.
pdf
R.Brown, P.J.Higgins, `Sur les complexes croises,
$\omega$-groupoides, et T-complexes', C R Acad Sci Paris Ser A 285 (1977)
997-999.
R.Brown, P.J.Higgins, `Sur les complexes croises
d'homotopie associee a quelque espaces filtree', C R Acad Sci Paris Ser A
286 (1978) 233-260.
R.Brown, P.J.Higgins, `The equivalence of
$\omega$-groupoids and cubical $T$-complexes', Cah. Top. Géom. Diff.
22, 349-370, 1981. pdf
R.Brown, P.J.Higgins, `The equivalence of $\infty$-groupoids
and crossed complexes', Cah. Top. Géom. Diff. 22, 371-386,
1981. pdf
R.Brown, P.J.Higgins, `Cubical abelian groups with connections are equivalent
to chain complexes', Homology, Homotopy and Applications, 5(1) (2003) 49-52.
R.Brown, J. Huebschmann, `Identities among relations', in Low-dimensional
topology, ed. R.Brown and T.L.Thickstun, London Math. Soc. Lect. Notes 46,
Cambridge University Press, 153-202, 1982.
R. Brown, I. Icen, `Homotopies and automorphisms of
crossed modules of groupoids', Applied Categorical Structures, 11 (2003)
185-206. pdf
R. Brown, I. Icen, `Towards
a 2-dimensional notion of holonomy', Advances in Math, 178 (2003)
141-175. pdf
R.Brown, G. Janelidze, ` Van Kampen theorems for categories of covering morphisms
in lextensive categories', J. Pure Appl. Algebra 119 (1997) 255-263.
R.Brown, G. Janelidze, `Galois theory of second order covering maps of simplicial
sets', J. Pure Appl. Algebra, 135 (1999) 83-91.
R.Brown, G. Janelidze, `Galois Theory and a new homotopy
double groupoid of a map of spaces', Applied Categorical Structures 12 (2004)
63-80.
R.Brown, D.L.Johnson, E.F.Robertson, `Some computations of non-abelian tensor
products of groups', J. Algebra, 111, 177-202, 1987.
R.Brown, J.-L.Loday, `Van Kampen theorems for diagrams
of spaces', Topology, 26, 311-335, 1987.
pdf
R.Brown, J.-L.Loday, `Homotopical excision, and Hurewicz theorems, for $n$-cubes
of spaces', Proc. London Math. Soc. (3), 54, 176-192, 1987.
pdf
R.Brown, K.C.H.Mackenzie, `Determination of a double Lie
groupoid by its core diagram', J. Pure Appl. Algebra 80, 237-272, 1992.
[Here
for postscipt file]
R. Brown, G.H. Mosa, `Double categories, 2-categories,
thin structures and connections', Theory and Applications of Categories 5
(1999) 163-175.
R.Brown, O.Mucuk, `Covering groups of non-connected topological groups
revisited', Math. Proc. Camb. Phil. Soc. 115, 97-110, 1994.
pdf
R. Brown, R.Paton and T. Porter, `Categorical language
and hierarchical models for cell systems', Computation
in Cells and Tissues - Perspectives and Tools of Thought, Paton, R.; Bolouri,
H.; Holcombe, M.; Parish, J.H.; Tateson, R. (Eds.) Natural Computing Series,
Springer (2004) 289-303.
R. Brown, T. Porter, `On the
Schreier theory of non-abelian extensions:
generalisations and computations', Proceedings Royal Irish Academy, 96 (1996)
213-227. pdf
R. Brown and T. Porter, `Category theory and higher dimensional algebra:
potential descriptive tools in neuroscience', Proceedingsof the International
Conference on Theoretical Neurobiology, Delhi, February
2003, edited by Nandini Singh, National Brain Research Centre, Conference
Proceedings 1 (2003) 80-92. UWB Preprint 03.05
R. Brown and T. Porter, `Category Theory: an abstract setting for
analogy and comparison', Advanced Studies in Mathematics
and Logic (to appear) UWB Preprint 05.10 .
pdf
R.Brown, A. Razak Salleh, `Free crossed resolutions of groups and presentations
of modules of identities among relations', Bangor
Preprint 1997, 20pp. LMS J. Comp. and
Math. 2 (1999) 28-61.
R.Brown, C.B.Spencer, `$\cal G$-groupoids, crossed modules, and the classifying
space of a topological group', Proc. Kon. Akad. v. Wet. 79, 296-302, 1976.
R.Brown, A.Tonks, `Calculation with simplicial and cubical groups in Axiom',
J. Symbolic Computation 17, 159-179, 1994.
R.Brown and C.D.Wensley, `On finite induced crossed modules and the homotopy
2-type of mapping cones', Theory
Appl. Categories, 3, 54-71, 1995.
R.Brown and C.D.Wensley, `Computing crossed modules induced by an inclusion
of a normal subgroup, with applications to homotopy 2-types',
Theory Appl. Categories, 2, 3-16,
1996.
R.Brown and C.D.Wensley,
`Computation and homotopical applications of induced crossed modules', J.
Symbolic Computation 35 (2003) 59-72.
R. A. Brown, ` Generalised group presentations', Trans. Amer. Math. Soc.,
334, 519-549, 1992.
M.Bullejos, A.M.Cegarra, J.Duskin, `On cat$^n$-groups and homotopy types',
J. Pure Appl. Algebra 86 (1993) 135-154.
M.Bullejos, P. Carrasco, A.Cegarra, `Cohomology with coefficients in symmetric
cat$^n$-groups. An extension of Eilenberg-Mac Lane's classification theorem.'
Granada Preprint, 1992.
J.S. Carter, M. Saito, `Knotted surfaces, braid movies and beyond', Preprint,
University of Texas at Austin, 1993.
Jean-Louis Cathelineau, `Birapport et groupoides',
Enseign. Math., II. Ser. 41, No.3-4, 257-280 (1995).
\v{C}ech, E. `H\"{o}herdimensionale homotopiegruppen',
Verhandlungen des Internationalen Mathematiker-Kongresses Zurich, Band
2, (1932) 203.
D. Conduché, `Modules croisés
généralisés de longeur 2', J. Pure Appl. Algebra, 34
(1984) 155-178.
D. Conduché, G.J.Ellis, `Quelques propriétés homologiques
des modules précroisés', J. Algebra, 123, 327-335, 1989.
D.Conduché, C.Rodriguez-Fernandez, `Non-abelian tensor and exterior
products and universal $q$-central relative extensions', J. Pure Appl. Algebra
78, 139-160, 1992.
A. Connes,Non commutative geometry, Academic
Press, 1994.
J.-M.Cordier, T.Porter, `Fibrant diagrams, rectifications and a construction
of Loday', J. Pure Appl. Algebra 67, 111-124, 1990.
S.J. Crans, On combinatorial models for higher dimensional homotopies,
Doctoral thesis, Utrecht, 1995.
N.K. Dakin, Kan complexes and multiple groupoid
structures, University of Wales, Bangor, Ph D Thesis (1997).
A.J.Duncan, G.J.Ellis, N.D.Gilbert, `A Mayer-Vietoris sequence in group homology
and the decomposition of relation modules', Glasgow Math. J. 37 (1995) 159-171.
P.J.Ehlers and T. Porter, `From simplicial groupoids to crossed complexes',
UCNW Maths Preprint 92.19, 35pp, 1992.
P.J.Ehlers and T. Porter, Varieties of simplicial groupoids I: Crossed complexes,
J Pure and Applied Algebra 120 (1997) 221-233.
P.J.Ehlers and T. Porter, Varieties of simplicial groupoids I: Crossed complexes,
erratum, J Pure and Applied Algebra 1999, Vol.134, No.2, pp.207-209
G.J.Ellis, `The non-abelian tensor product of finite groups is finite', J.
Algebra, 111, 203-205, 1987.
G.J.Ellis, `Non-Abelian exterior products of groups and exact sequences in
the homology of groups', Glasgow Math. J., 29, 13-19, 1987a.
G.J.Ellis, `Non-Abelian exterior products of Lie algebras and an exact sequence
in the homology of Lie algebras', J. Pure Appl. Algebra, 46, 111-115, 1987c.
G.J.Ellis, `Higher dimensional crossed modules of
algebras', J. Pure Applied Algebra, 52, 277-282, 1988.
G.J.Ellis, `Multirelative algebraic $K$-theory:
the group$K_2(\Lambda;I_1,\ldots ,I_n)$ and related computations', J. Algebra
112, 271-289, 1988.
G.J.Ellis, `An algebraic derivation of a certain exact sequence', J. Algebra,
127, 178-181, 1989.
G.J.Ellis, `Relative derived functors and the homology of groups', Cah. Top.
Géom. Diff. Cat. 31, 121-135, 1990.
G.J.Ellis, `Relative derived contravariant functors and the
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P.J.Higgins, J.Taylor, `The fundamental groupoid and homotopy crossed complex
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C. Hog-Angeloni, W.Metzler, A.J.Sieradski, (Editors),
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D.L.Johnson, `The non-Abelian square of a finite split metacyclic group',
Proc. Edinburgh Math. Soc., 30, 91-95, 1987.
D.W.Jones, Polyhedral $T$-complexes, University
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K.H. Kamps and T. Porter, Abstract homotopy and simple homotopy theory.
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L.-C. ,Kappe, `Non abelian tensor products of groups:
the commutator connection', Proceedings Groups St Andrews 1997 at Bath, LMS
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L.-C. Kappe and M.P Visscher, `Two generator two-groups
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M.M.Kapranov, V.Voevodsky, `Combinatorial-geometric aspects of polycategory
theory: pasting schemes and higher Bruhat orders (list of results)', Cah.
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M.M.Kapranov, V. Voevodsky, `$\infty$-groupoids and homotopy types' Cah.
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M.M.Kapranov, V. Voevodsky, `2-categories and Zamolodchikov tetrahedra
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2, 177-259, 1994.
J.-L. Loday and D. Guin-Walery, `Obstruction a l'excision
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J.-H.Lu, A.Weinstein, `Groupoïdes symplectiques
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K.C.H.Mackenzie, `Classification of principal bundles and Lie groupoids with
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K.C.H.Mackenzie, `Double Lie algebroids and second order
geometry, I', Advances in Math., 94 (1992) 180-239.
K.C.H.Mackenzie, `Double Lie algebroids and second order geometry, II', preprint,
1996 (27 pages).
G. W. Mackey, `Ergodic theory and virtual groups',
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I.Moerdijk, J-A Svensson, `Algebraic classification of equivariant homotopy
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G.Nan Tie, `A Dold-Kan theorem for crossed complexes'
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G.Nan Tie, `Iterated $W$ and $T$-groupoids', J. Pure Appl. Algebra, 56, 195-209,
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K.Norrie, `Actions and automorphisms of crossed modules',
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T.Porter, `Extensions, crossed modules and internal categories in categories
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T.Porter, `n-types of simplicial groups and crossed
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T. Porter, Interpretations of Yetter's notion of G-colouring: simplicial
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S.J.Pride, `Identities among relations of group presentations', in E.Ghys,
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J. Shrimpton, `Some groups related to the symmetry of a directed graph',
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Carlos Simpson, `A closed model structure for n-categories, internal $Hom$,
n-stacks and generalized Seifert-Van Kampen', 67 pages,
http://xxx.soton.ac.uk/abs/alg-geom/9704006
C. B.~Spencer, `An abstract setting for homotopy pushouts and pullbacks',
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