We now have some material available on the world wide web for downloading as postscript files. The School of Mathematics, University of Wales, Bangor may be accessed at http://www.bangor.ac.uk/ma/ The following papers are available as postcript files via R. Brown's home page http://www.bangor.ac.uk/~mas010/home.html R. Brown and W. Dreckmann, ``Domains of data and domains of terms in AXIOM''. Abstract: This gives a general account and the source Axiom 2.0 code for directed graphs, free categories, free groupoids, which will give an impression of coding in Axiom. R. Brown and O. Mucuk, ``The monodromy groupoid of a Lie groupoid'', {\em Cah. Top. G\'eom. Diff. Cat}, 36 (1995) 345-369. Abstract: We show that under general circumstances, the disjoint union of the universal covers of the stars of a Lie groupoid admits the structure of a Lie groupoid, such that the projection has a monodromy property on the extension of local smooth morphisms. This completes a detailed account of results announced by J Pradines. R. Brown and O. Mucuk, ``Foliations, locally Lie groupoids, and holonomy'', {\em Cah. Top. G\'eom. Diff. Cat}, (1996) (to appear). Abstract: We show that a paracompact foliated manifold determines a locally Lie groupoid (or piece of a differentiable groupoid, in the sense of Pradines). This allows for the construction of holonomy and monodromy groupoids of a foliation to be seen as particular cases of constructions for locally Lie groupoids. R. Brown, ``Representation and computation for crossed modules'', Proceedings {\em Cat\'egories, Algebres, Esquisses, Neo-esquisses}, Caen, 1994, 6pp. Abstract: We argue for the need to develop `structural computation', to handle the translation of algebraic structures between equivalent categories. This is illustrated with the problem of the tensor product in the equivalent categories of crossed modules over groupoids, double groupoids with connection, 2-groupoids. R. Brown, M. Golasinski, T.Porter, and A.P.Tonks, ``On function spaces of equivariant maps and the equivariant homotopy theory of crossed complexes.'' 18pp Abstract: This paper gives an equivariant version of the homotopy theory of crossed complexes for the case of a discrete group action. The applications generalise work on equivariant Ellenberg-MacLane spaces, including the non-abelian case of dimension 1, and on local systems. It also generalises the theory of equivariant 2-types, due to Moerdijk and Svensson. Further we give results not just on the homotopy classification of maps, but also on the homotopy types of certain equivariant function spaces. (Indag. Math. (to appear)) R. Brown and T. Porter, ``On the Schreier theory of non-abelian extensions: generalisations and computations'', 21pp Abstract: Classically, a Schreier 2-cocycle for a group G involves functions on the 3-fold and 2-fold products of G with itself. We show how a crossed resolution may be used to give smaller and more computable presentations of such cocycles, which are determined by a presentation of G and identities among relations. This is a modern expression of ideas of Turing, 1938. R. Brown and C.D.Wensley, ``Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types'', 9pp Abstract: We suppose M, P are normal subgroups of a group Q and prove directly a value for the crossed Q-module induced from the crossed P-module M by the inclusion of P in Q. Using methods of free crossed resolutions, we calculate explicitly the k-invariant of this induced crossed module, in the case when Q/P is finite cyclic. We also use coproducts of crossed P-modules to obtain some general results on induced crossed modules, again when P is normal in Q. These results are applied to the 2-type of homotopy pushouts of certain maps of classifying spaces of discrete groups. This continues work of a previous paper, published in TAC, 1995, no.3. R. Brown and G. Janelidze, ``Van Kampen theorems for categories of covering morphisms in lextensive categories'', 9pp, (J. Pure Applied Algebra, to appear). Abstract: We show that lextensive categories are a natural setting for statements and proofs of the ``tautologous'' Van Kampen theorem, in terms of coverings of a space. R. Brown and G. Janelidze, ``Galois theory of second order covering maps of simplicial sets'', 10pp, submitted, 1995. Abstract: We give a version for simplicial sets of a second order notion of covering map, which bears the same relation to the usual coverings as do groupoids to sets. The Generalised Galois theory of the second author yields a classification of such coverings by the action of a certain kind of double groupoid. The following papers are available as postcript files via T. Porter's home page http://www.bangor.ac.uk/~mas013/home.html Bangor Maths Preprint No. 95.08 Spaces of maps into classifying spaces for equivariant crossed complexes. Authors: R. Brown, M. Golasinski, T. Porter, and A. Tonks September 13, 1995 (see above) Keywords: Equivariant homotopy, crossed complexes AMS Subject Classification: 55P91, 55U10, 55U35 Bangor Maths Preprint No.95.09 Title: Categorical Aspects of Equivariant Homotopy Authors:.-M. Cordier and T. Porter Date: September 13, 1995 Abstract: Using the theory of homotopy coherent Kan extensions, results of Elmendorf and Dwyer and Kan are generalised. This produces simplicially enriched equivariant versions of the singular complex / geometric realisation adjunction of the non- equivariant theory. Keywords: Homotopy coherent Kan extension, simplicially enriched categories, G-equivariant homotopy AMS Subject Classification: 55P91, 18G55, 18D20, 18G30 Type of file: LATEX or dvi No. of pages: 18 Bangor Maths Preprint No. 95.10 Title: Homotopy coherent category theory Authors: J.-M. Cordier and T Porter Abstract: This article is an introduction to the categorical theory of homotopy coherence. It is based on the construction of the homotopy coherent analogues of end and coend, extending ideas of Meyer and others. The paper aims to develop homotopy coherent analogues of many of the results of elementary category theory, in particular it handles a homotopy coherent form of the Yoneda lemma and of Kan extensions. This latter area is linked with the theory of generalised derived functors. Keywords: Simplicially enriched categories, Homotopy coherent ends and coends, Yoneda lemma AMS Subject Classification: 18D20, 18D05, 18G30, 18A99 Type of file: dvi, or Postscript No. of pages: 54 Bangor Maths Preprint No. 95.11 Title: Interpretations of Yetter's notion of G-coloring: simplicial fibre bundles and non-abelian cohomology Authors: T Porter Date: October 11, 1995 Abstract: This paper notes and explores the connection between Yetter's notion of G-coloring where G is either a finite group or a finite `Categorical group' and the theory of simplicial fibre bundles. This allows an interpretation of Yetter's topological quantum field theory in terms of equivalence classes of simplicial fibre bundles. If G is a finite categorical group, these fibre bundles have interesting lifting properties and their fibres are groupoids. Using recent results and descriptions of non-abelian cohomology due to Breen and Duskin, these fibre bundles are linked with non-abelian cocycles with coefficients in G. Keywords: Topological Quantum Field Theory, fibre bundle, non- abelian cohomology AMS Subject Classification: 81T99, 57N70, 55R99 Type of file: Postscript or dvi. No. of pages: 30 Prof R. Brown School of Mathematics Dean St University of Wales Bangor Gwynedd LL57 1UT UK Tel: (direct) +44 1248 382474 (office) +44 1248 382475 Fax: +44 1248 355881 email: mas010@bangor.ac.uk wwweb: http://www.bangor.ac.uk/~mas010/home.html wwweb for maths: http: //www.bangor.ac.uk/ma