Homomorphisms of higher categories
نویسنده
چکیده
We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction is such that these homomorphisms admit a strictly associative and unital composition. We give two applications of this construction. The first is to tricategories; and here we do not obtain the trihomomorphisms defined by Gordon, Power and Street, but rather something which is equivalent in a suitable sense. The second application is to Batanin’s weak ω-categories. © 2010 Elsevier Inc. All rights reserved. MSC: 18D05; 55U35
منابع مشابه
Homomorphisms and Higher Extensions for Schur Algebras and Symmetric Groups
This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined.
متن کاملTriangular Witt Groups . Part I : the 12 - Term Localization Exact Sequence
To a short exact sequence of triangulated categories with duality, we associate a long exact sequence of Witt groups. For this, we introduce higher Witt groups in a very algebraic and explicit way. Since those Witt groups are 4-periodic, this long exact sequence reduces to a cyclic 12-term one. Of course, in addition to higher Witt groups, we need to construct connecting homomorphisms, hereafte...
متن کاملPosets with Projections and their Morphisms
This paper investigates function spaces of partially ordered sets with some directed family of projections. Given a xed directed index set (I;), we consider triples (D; ; (p i) i2I) consisting of a poset (D;) and a monotone net (p i) i2I of projections of D. We call them (I;)-indexed pop's (posets with projections). Our main purpose is to study structure preserving maps between (I;)-indexed pop...
متن کاملCommentationes Mathematicae Universitatis Carolinae
Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...
متن کاملBooleanization of uniform frames
Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...
متن کامل