The based ring of the lowest two-sided cell of an affine Weyl group. II
The branching nerve of HDA and the Kan condition.
The Brauer and Brauer-Taylor groups of a symmetric monoidal category
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The Cantor-Bernstein theorem for functors
The cartesian closed hull of the category of approach spaces
The cartesian closed topological hull of the category of completely regular filterspaces
The categories of presheaves containing any category of algebras [Book]
The category of Banach spaces in sheaves
The category of cofinite modules for ideals of dimension one and codimension one
The category of compactifications and its coreflections
We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone . A corCM implies the assignment to each locally compact, noncompact a compactification minimum for membership in the “object-range” of . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...
The category of connected partial unary algebras
The Category of Differential Triads
The category of disintegration
The category of groupoid graded modules
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...
The category of long exact sequences and the homotopy exact sequence of modules.
The category of nonindexed algebras and weak homomorphisms
The category of opetopes and the category of opetopic sets.
The category of Pawlak machines
The category of totally symmetric quasigroups is binding