CAHIERS DE TOPOLOGIE ET GEOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES

Fascicule 1: 3nd issue dedicated to J. Adamek

Karazeris & Velibil, Representability relative to a doctrine 3
Milius & Moss, Equational properties of recursive program scheme solutions 23
L. Sousa, On boundedness and small-orthogonality classes 67

Fascicule 2

E. Cheng & M. Makkai, A note on the Penon definition of n-category 83
M. Grandis, The role of symmetries in cubical sets and cubical categories 102
R. Guitart, Klein's group as a Borromean object 144
M. Bunge, J. Funk, M. Jibladze & T. Streicher, On the paper "Definable completeness" 156

Fascicule 3: 1st issue dedicated to F. Borceux

Foreword 163
M. Gran & G. Janelidze, Covering morphisms and normal extensions in Galois structures associated with Galois theories 171
R. Borger & R. Kemper, Infinitary linear combinations in reduced cotorsion modules 189
J. Rosicky, Are all cofibrantly generated model categories combinatorial? 233
D. Bourn & G. Janelidze, Centralizers in action accessible categories 211

Fascicule 4: 2nd issue dedicated to F. Borceux

M. Grandis, Limits in symmetric cubical categories (On weak cubical categories, II) 242
J. Adamek & M. Hebert, On quasi-equations in locally presentable categories 273
Z. Janelidze, Closedness properties of internal relations, VI: approximate operations 298

K. Kachour, Définition algébrique des cellules non strictes, 1
Golasinski & Stramaccia, Weak homotopy equivalences of mapping spaces and Vogt's Lemma, 69
R. Guitart, Toute théorie est algébrique et topologique, 83
A. Solomon, A note on Kieboom's Pullback Theorem for cofibrations, 129
A.C. Ehresmann, Fifty years of research, 142
The "Cahiers" on Internet, 153
Theory and Applications of Categories: Information on the electronic Journal TAC, 155

Fascicule 3 and 4: issues dedicated to J. Adámek

Borceux, Jung, Rosicky & Sousa, Foreword, 163
D. Bourn, The Mal'tsev operation on extensions, 176
Gran & Rodelo, A universal construction in Goursat categories, 196
Sichler & Trnkova, On clones determined by their initial segments, 209
W.Tholen, Injectivity versus exponentiability, 228
Borceux & Rosicky, On filtered weighted colimits of presheaves, 243
Herrlich, Keremedis & Tachtsis, Tychonoff products of super second countable and super separable metric spaces, 267
Janelidze & Sobral, Profinite relationl structures, 280
Koubek & Sichle, On synchronized relatively full embeddings and Q-universality, 289
A.H. Roque, Protomodular quasivarieties of universal algebras, 307
Resumes des articles parus dans le Volume XLIX, 315

Remark.
Issues 3 and 4 of the Volume XLIX are the first 2 parts of the Adamek Volume. Its last part is Volume L-1, of which the contents are:
Karazeris & Velebil, Representability relative to a doctrine, 3
Milius & Moss, Equational properties of recursive program scheme solutions, 23
L. Sousa, On boundedness and small-orthogonality classes, 67

Max Kelly, 2
N. Ganter, Smash products of E(1)-local spectra at an odd prime, 3
Golasinski, Goncalves & Wong, Equivariant evaluation subgroups and Rhodes groups, 55
F. Mynard, Unified characterization of exponential objects in TOP, PRTOP and PARATOP, 70
G.E. Reyes, Embedding manifolds with boundary in smooth toposes, 83
Bourn & Rodelo, Cohomology without projectives, 104
Theory and Applications of Categories: Information on the electronic journal TAC, 155
Grandis & Pare, Lax Kan extensions for double categories, 163
A. Solomon, A category model proof of the Cogluing Theorem, 200
Coquand, Lombardi & Schuster, The projective spectrum as a distributive lattice, 220
I. Kolar, On special types of nonholonomic jets, 228
New book: Memory Evolutive Systems by Ehresmann and Vanbremeersch, 238
Colebunders & Gerlo, Firm reflections generated by complete metric spaces, 243
R. Guitart, An anabelian definition of abelian homology, 261
A.C. Ehresmann, Sur Paulette Libermann (1919-2007), 270
A.C. Ehresmann, Fiftieth anniversary of the "Cahiers", 275
Index of the "Cahiers" I to XLVIII, 278
Resumes des articles parus dans le Volume XLVIII, 317

Kock & Reyes, Distributions and heat equation in SDG, 2-28
R. Attal, Combinatorial stacks and the four-color Theorem, 29-49
S. Niefield, Homotopic pullbacks, lax pullbacks and exponentiability, 50-80
Dubuc & Street, A construction of 2-filtered bicolimits of categories, 83-106
M. Grandis, Lax 2-categories and directed homotopy, 107-128
H. Nishimura, Synthetic Differential Geometry of higher-order differentials, 129-154 et 207-232
Jibladze & Pirashvili, Quillen cohomology and Baues-Wirsching cohomology of algebraic structures, 163-205
C. Townsend, A categorical proof of the equivalence of local compactness and exponentiability in locale theory, 233-239
Barkhudaryan, Koubek & Trnkova, Structural properties of endofunctors, 242-260
R. Garner, Double clubs, 261-317
RÉSUMÉS des articles parus dans le Volume XLVII, 318-320.

Bourn & Penon, Catégorification de structures définies par monade cartésienne, 2
M. Grandis, Equilogical spaces, homology and non-commutative geometry, 53
Dubuc & Zilber, Weil prolongations of Banach manifolds in an analytic model of SDG, 83
I. Stubbe, Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories,99
M. Lawson, Constructing ordered groupoids,123
Bridges, Ishihara, Schuster & Vita, Products in the category of apartness spaces, 139
RESUMES DU COLLOQUE INTERNATIONAL "Charles Ehresmann : 100 ans" (Amiens, Octobre 2005), 163
W.D. Garraway, Sheaves for an involutive quantaloid, 243
Giuli & Slapal, Raster convergence with respect to a closure operator, 275
B. Banaschewski, Projective frames: a general view, 301
Guide to authors, 313

N. Ball & A. Pultr, Forbidden forests in Priestley spaces, 2-22.
J. Kubarsi & T. Rybicki, Local and nice structures of the groupoid of an equivalence relation, 23-34.
Dawson, Paré & Pronk, Free extensions of double categories, 35-80.
Lawson & Sieinberg, Ordered groupoids and etendues, 82-108.
D-C. Cisinski, Le localisateur fondamental minimal, 109-140.
Centazzo, Rosicky & Vitale, A characterization of locally D-presentable categories, 141-146.
Ebrahimi, Tabatabaee & Mahmoudi, Metrizability of ?-frames, 147-156.
Y. Kopylov, Exact couples in a Raikov semi-abelian category, 162-178.
Adams & van der Zypen, Representable posets and their order components, 179-192.
Grandis & Pare, Adjoint for double categories, 193-240.
Bunge, Funk, Jibladze & Streicher, Definable completeness, 243-266.
A. Frolicher, Axioms for convenient calculus, 267-286.
Kruml & Resende, On quantales that classify C*-algebras, 287-296.
D. van der Zypen, Order convergence and compactness, 297-300.
Guo, Sobral & Tholen, Descent equivalence, 301-315.

Johnson & McCarthy, A classification of degree n functors, I 2 M. MacKaay, Note on the holonomy of connections in twisted bundles, 39
Bullejos, Faro & M.A. Garcia-Munoz, Homotopy colimits and cohomology with local coefficients, 63
Theory and Applications of Categories: Information on the electronic Journal TAC 82
A. Kock, The stack quotient of a groupoid, 85
Fiedorowicz & Vogt, Simplicial n-fold monoidal categories model all loop spaces, 105
I. Kolar, A general point of view to nonholonomic jet bundles, 149
Johnson & McCarthy, A classification of degree n functors, II 163
Barkhudaryan, El Bashir & Trnkova, Endofunctors of Set and cardinalities, 217
Biographie de René Lavendhomme, 242 242
Garzon & del Rio, Low-dimensional cohomology for categorical groups 247
M. Grandis, Directed homotopy Theory, I 281
Resumés des articles parus dans le Volume XLIV 317

Alvarez, Vilaboa, Rodriguez & Novoa, About the naturality of Beattie's Decomposition Theorem with respect to a change of Hopf Algebras, 2
J. Paseka, A note on nuclei of quantale modules, 19
A. Frölicher, Linear spaces and involutive duality functors, 35
V. Lyubashenko, Tensor product of categories of equivariant perverse sheaves, 49
Adamek, Herrlich, Rosicky & Tholen, On a generalized small-object argument for the injective subcategory problem, 83
P. Gaucher, About the globular homology of higher dimensional automata, 107
Theory and Applications of Categories: Information on the electronic Journal TAC, 157
Moens, Berni-Canani & Borceux, On regular presheaves and regular semi-categories, 163
R. Leclercq, Symétries de Hecke à déterminant associé central, 191
P. Kainen, Isolated squares in hypercubes and robustness of commutativity, 213
T. Pirashvili, On the PROP corresponding to bialgebras, 221
L. Stramaccia, Shape and strong shape equivalences, 242
B. Toen, Vers une interprétation galoisienne de la théorie de l'homotopie, 257
Y.T. Rhineghost, The boolean prime ideal theorem holds iff maximal open filters exist, 313
Résumés des articles parus dans le Volume XLIII 317

P. Akueson, Géométrie de l'espace tangent sur l'hyperboloïde quantique, 2
Hebert, Adamek & Rosicky, More on orthogonality in locally presentable categories, 51
M. Golasinski & D. Lima Gonçalves, Equivariant Gottlieb groups, 83
M. Grandis, Higher fundamental functors for simplicial sets, 101
S. Piccarreta, Rational nilpotent groups as subgroups of self-homotopy equivalences, 137
W. Rump, Almost abelian categories, 163
Barr & Kleisli, Correction to "Topological balls", 227
P. Ageron, Esquisses inductives et presque inductives, 229
E. Lowen-Colebunders, R. Lowen & M. Nauwelaerts, The cartesian closed hull of the category of approach space, 242
S. Klaus, Cochain operations and higher cohomology operations, 261
M. Sioen, Symmetric monoidal closed structures in PRAP, 285
Résumés des articles parus dans le Volume XLII, 317

S. CRANS, On braidings, syllepses, and symmetries, 2
ALVAREZ & VILABOA, On Galois H-objects and invertible H*-modules, 75
DUBUC & ZILBER, Infinitesimal and local structures for Banach spaces and its exponentials in a topos, 82
D. HOLGATE, Completion and closure, 101
PULTR & THOLEN, Localic enrichments of categories, 121
L. SCHRÖDER, Isomorphisms and splitting of idempotents in semicategories, 143
NOUVEAU LIVRE: Cours d'Analyse 3, par Chatterj, 154
Theory and Applications of Categories: Information on the electronic Journal TAC, 157
P. BOOTH, Fibrations and classifying spaces: overview and the classical example, 162
DUBUC & ZILBER, Inverse function theorems for Banach spaces in a topos, 207
PULTR & SICHLER, A Priestley view on spatialization of frames, 225
NOUVEAU LIVRE: Gödel: une révolution en mathématiques, par A. Delessert, 239
M. BARR, On *-autonomous categories of topological vector spaces, 243
N. S. YANOFSKY, The Syntax of coherence, 255
MOENS & VITALE, Groupoids and the Brauer group, 305
Addendum à D. HOLGATE, Completion and closure, 314
RESUMES des articles parus dans le Volume XLI, 316

M. BARR & H. KLEISLI, Topological balls, 3
DOUPOVEC & KOLÁR, On the jets of fibered manifold morphisms, 21
J. PENON, Approche polygraphique des infini-catégories non strictes, 31
GARCIA ROMÁN, MÁRQUEZ HERNÁNDEZ, JARA & VERSCHOREN, Uniform filters 82
A. KOCK & G. REYES, A Note on frame distributions 127
DAMPHOUSSE & GUITART, Liftings of Stone's monadicity to spaces and the duality between the calculi of inverse and direct images 141
Theory and Applications of Categories: Information on the electronic Journal TAC 158
M. GRANDIS & R.PARÉ, Limits in double categories 162
H. HERRLICH & L. SCHRODER, Composing special epimorphisms and retractions 221
D.-C. CISINSKI, La classe des morphismes de Dwyer n'est pas stable par rétractes 227
E. DAVID, Stone spaces of more partially ordered sets 233
Kyung Chan MIN, Young Sun KIM & Jin Won PARK, Fibrewise exponential laws in a quasi-topos 242
MUTLU & PORTER, Free crossed resolutions from simplicial resolutions with given CW-basis 261
E. VITALE, Multi-bimodels 283
D. BOURN, Baer sums and fibered aspects of Malc'ev operations 297
RESUMES des articles parus dans le Volume XL 317

CRANE & YETTER, Examples of categorification, 3
S. MANTOVANI, Semilocalizations of exact and Lextensive categories, 27
CAVICCHIOLI, HEGENBARTH & SPAGGIARI, Topological properties of high-dimensional handles, 45
PULTR & SICHLER, Finite commutative monoids of open maps, 63
P.I. BOOTH, Fibrations and classifying spaces: an axiomatic approach, 83
DUBUC & ZILBER, Banach spaces in an analytic model of SDG, 117
GRANDJEAN & VITALE, Morita equivalence for regular algebras, 137
CRANE & YETTER, Deformations of (bi)tensor categories, 163
P.I. BOOTH, Fibrations and classifying spaces: An axiomatic Approach II, 181
BORCEUX & CRUCIANI, Skew omega-sets coincide with omega-poset, 205
P. CRISTOFORI, Heegard and regular genus agree for compact 3-manifolds, 221
J. BICHON, Trivialisations dans les catégories tannakiennes, 243
P.I. BOOTH, On the geometric bar construction and the Brown Representability Theorem, 271
GRAN & VITALE, On the exact completion of the homotopy category, 287
INDEX des Volumes XXVI à XXXIX (1985-1998), 307

M.A. BATANIN, Categorical strong shape theory, 3
J.G. CABELLO, Simplicial groups as models for n-types, 67
GARZON & MIRANDA, Homotopy theory for (braided) Cat-groups, 99
CASALI & MALAGOLI, Handle-decompositions of PL 4-manifolds, 141
K.I. ROSENTHAL, Relational monoids, multirelations, and quantalic recognizers, 161
G.M. KELLY & I.J. LE CREURER, On the monadicity over Graphs of categories with limits, 179
J.-L. BRYLINSKI, Central extensions and reciprocity laws, 193
J. ADAMEK & M.-C. PEDICCHIO, A remark on topological spaces, grids and topological system,s 217
P. KARAZERIS, Compact topologies on locally presentable categories, 227
E. LOWEN, R. LOWEN & VERBEECK, Exponential objects in the construct PRAP, 259
D. DIKRANJAN & J. PELANT, Categories of topological spaces with sufficiently many sequentially closed spaces, 277
M. GRANDIS, Weak subobjects and weak limits in categories and homotopy categories, 301

The "Cahiers" are a quarterly Journal with one Volume a year (divided in 4 issues). They publish original papers in Mathematics, the center of interest being the Theory of Categories and its applications, specially in Topology and Differential Geometry. Papers submitted for publication should be sent to one of the editors. Authors can obtain detailed information on submission format from the "Guide to Authors" published in each issue of the "Cahiers". An Index of all the papers published in the "Cahiers" since their creation, as well as English abstracts of the papers published since 1999 can be found at the URL:
http://perso.wanadoo.fr/vbm-ehr/CT/
All the papers published in former volumes of the "Cahiers" (up to volume XLVII) are now freely available online on the NUMDAM site: http://www.numdam.org/numdam-bin/feuilleter?j=CTGDC&sl=0

A.C. Ehresmann, Faculté de Math. et Info., Amiens. Andree.Ehresmann@u-picardie.fr
J. Adamek, Technical University Braunschweig: adamek@iti.cs.tu-bs.de
M. Bunge, McGill University, Montreal: bunge@math.mcgill.ca
R. Guitart, U.F.R. de Math., Université Paris 7: guitart@maths.jussieu.fr
P. Johnstone, University of Cambridge, G.-B: ptj@dpmms.cam.ac.uk
A. Kock, Aarhus Universitet, Denmark: kock@imf.au.dk
T. Porter, University College of North Wales, Bangor: t.porter@bangor.ac.uk.
J. Pradines, Université Paul Sabatier, Toulouse: pradines@picard.ups.tlse.fr
R. Street, Macquarie University, Australie: street@math.mq.edu.au

All backsets of the "Cahiers" are still available, as well as the Supplements, published from 1980 to 1984, devoted to the collected works of the mathematician Charles Ehresmann (1905-1979), who created the "Cahiers" in 1958. These Supplements consist of 7 books, and may be obtained soft or cloth covered. They contain all the articles of C. Ehresmann, with long comments (in English) updating these papers.

Correspondence concerning subscriptions is to be sent to

Mme Ehresmann, Faculté de Math. et Info.,
33 rue Saint-Leu, F-80039 Amiens. France.
E-mail: Andree.Ehresmann@u-picardie.fr

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