ISSN 1201-561X
T A C
6
THEORY AND APPLICATIONS OF CATEGORIES
Volume 31, 2016
The Euler characteristic of an enriched category
Kazunori Noguchi and Kohei Tanaka 1
The heart of a combinatorial model category
Zhen Lin Low 31
On the magnitude of a finite dimensional algebra
Joseph Chuang, Alastair King and Tom Leinster 63
A two-dimensional Birkhoff’s theorem
Matej Dostal 73
Enriched algebraic theories and monads for a system of arities
Rory B. B. Lucyshyn-Wright 101
Relative symmetric monoidal closed categories I: Autoenrichment and change of base
Rory B. B. Lucyshyn-Wright 138
Transfinite limits in topos theory
Moritz Kerz 175
A characterization of central extensions in the variety of quandles
Valrian Even, Marino Gran and Andrea Montoli 201
On biadjoint triangles
Fernando Lucatelli Nunes 217
Some insights on bicategories of fractions: representations and compositions of 2-morphisms
Matteo Tommasini 257
c The Editors of Theory and Applications of Categories 2016. Permission to copy for private use granted.
Theory and Applications of Categories,Vol. 31 ii
Stacks and sheaves of categories as fibrant objects, II
Alexandru E. Stanculescu 330
Spectra of compact regular frames
Guram Bezhanishvili, David Gabelaia, Mamuka Jibladze 365 A cotriple construction of a simplicial algebra used in the definition
of higher Chow groups
Jason Polak 384
Construction of categorical bundles from local data
Saikat Chatterjee, Amitabha Lahiri and Ambar N. Sengupta 388 Partial linearity and partial natural Mal’tsevness
Dominique Bourn 418
Relative internal actions
James Richard Andrew Gray and Tamar Janelidze-Gray 444
Right delocalization of model categories
Bruce R Corrigan-Salter 462
The morphism axiom for n-angulated categories
Emilie Arentz-Hansen, Petter Andreas Bergh and Marius Thaule 477 The snail lemma
Enrico M. Vitale 484
Linear structures on locales
Pedro Resende and Joao Paulo Santos 502
Representation and character theory of finite categorical groups
Nora Ganter and Robert Usher 542
Classical and relative realizability
Jaap van Oosten and Tingxiang Zou 571
The linearity of traces in monoidal categories and bicategories
Kate Ponto and Michael Shulman 591
The local Joyal model structure
Nicholas J. Meadows 690
Homotopy locally presentable enriched categories
Stephen Lack and Jiri Rosicky 712
Compact closed bicategories
Michael Stay 755
Strict ω-categories are monadic over polygraphs
Francois Metayer 799
Theory and Applications of Categories,Vol. 31 iii
The Fermat functors
Enxin Wu 807
Enriched Yoneda lemma
Vladimir Hinich 833
Projectivity, continuity and adjointness: quantales, Q-posets and Q-modules
Susan Niefield 839
Tannaka theory over sup-lattices and descent for topoi
Eduardo J. Dubuc and Martin Szyld 852
On the representations of 2-groups in Baez-Crans 2-vector spaces
Benjamin A. Heredia and Josep Elgueta 907
Compositories and gleaves
Cecilia Flori and Tobias Fritz 928
On Evrard’s homotopy fibrant replacement of a functor
Boris Shoikhet 989
Monads on dagger categories
Chris Heunen and Martti Karvonen 1016
Products of families of types and (Π, λ)-structures on C-systems
Vladimir Voevodsky 1044
A functorial approach to Dedekind completions and the representation of vector lattices and l-algebras by normal functions
G. Bezhanishvili, P. J. Morandi, B. Olberding 1095
Cosheafification
Andrei V. Prasolov 1134
THEORY AND APPLICATIONS OF CATEGORIES (ISSN 1201-561X) will disseminate articles that significantly advance the study of categorical algebra or methods, or that make significant new contribu- tions to mathematical science using categorical methods. The scope of the journal includes: all areas of pure category theory, including higher dimensional categories; applications of category theory to algebra, geometry and topology and other areas of mathematics; applications of category theory to computer science, physics and other mathematical sciences; contributions to scientific knowledge that make use of categorical methods.
Articles appearing in the journal have been carefully and critically refereed under the responsibility of members of the Editorial Board. Only papers judged to be both significant and excellent are accepted for publication.
Full text of the journal is freely available in .dvi, Postscript and PDF from the journal’s server at http://www.tac.mta.ca/tac/and by ftp. It is archived electronically and in printed paper format.
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Information for authors. The typesetting language of the journal is TEX, and LATEX 2ε is strongly encouraged. Articles should be submitted by e-mail directly to a Transmitting Editor. Please obtain detailed information on submission format and style files fromhttp://www.tac.mta.ca/tac/.
Managing editor. Robert Rosebrugh, Mount Allison University: [email protected]
TEXnical editor. Michael Barr, McGill University: [email protected]
Assistant TEX editor. Gavin Seal, Ecole Polytechnique F´ed´erale de Lausanne:
gavin [email protected]
Transmitting editors.
Clemens Berger, Universit´e de Nice-Sophia Antipolis: [email protected] Richard Blute, Universit´e d’ Ottawa: [email protected]
Lawrence Breen, Universit´e de Paris 13: [email protected]
Ronald Brown, University of North Wales: ronnie.profbrown(at)btinternet.com Valeria de Paiva: Nuance Communications Inc: [email protected] Ezra Getzler, Northwestern University: getzler(at)northwestern(dot)edu Kathryn Hess, Ecole Polytechnique F´ed´erale de Lausanne: [email protected] Martin Hyland, University of Cambridge: [email protected]
Anders Kock, University of Aarhus: [email protected]
Stephen Lack, Macquarie University: [email protected]
F. William Lawvere, State University of New York at Buffalo: [email protected] Tom Leinster, University of Edinburgh: [email protected]
Ieke Moerdijk, Utrecht University: [email protected] Susan Niefield, Union College: [email protected] Robert Par´e, Dalhousie University: [email protected] Jiri Rosicky, Masaryk University: [email protected]
Giuseppe Rosolini, Universit`a di Genova: [email protected] Alex Simpson, University of Ljubljana: [email protected] James Stasheff, University of North Carolina: [email protected] Ross Street, Macquarie University: [email protected] Walter Tholen, York University: [email protected]
Myles Tierney, Universit´e du Qu´ebec `a Montr´eal : [email protected] R. J. Wood, Dalhousie University: [email protected]
