We deene the continuum up to order isomorphism (and hence homeomorphism) as the nal coalgebra of the functor X !, ordinal product with !. This makes an attractive analogy with the deenition of the ordinal ! itself as the initial algebra of the functor 1; X, prepend unity, with both deenitions made in the category of posets. The variants 1; (X !), X o !, and 1; (X o !) yield respectively Cantor ...

Given a smooth projective varietyX , we denote byD(X) the bounded derived category of coherent sheaves D(Coh(X)). All varieties we consider below are over the complex numbers. A result of Rouquier, [Ro] Théoréme 4.18, asserts that if X and Y are smooth projective varieties with D(X) ' D(Y ) (as linear triangulated categories), then there is an isomorphism of algebraic groups Aut(X)× Pic(X) ' Au...

We show that the weighted fusion category algebra of the principal 2-block b0 of GL2(q) is the quotient of the q-Schur algebra S2(q) by its socle, for q an odd prime power. As a consequence, we get a canonical bijection between the set of isomorphism classes of simple kGL2(q)b0-modules and the set of conjugacy classes of b0-weights in this case.

This paper is a part of the series [KL]; however, it can be read independently of the first two parts. In [D3], Drinfeld proved the existence of an equivalence between a tensor category of representations of a quantum group over C[[ ro]] and a tensor category of representations of an undeformed enveloping algebra over C[[ro]] , in which the associativity constraints are given by the Knizhnik-Za...

In previous work [7], the authors constructed and studied a lift of the Galois correspondence to stable homotopy categories. In particular, if L/k is a nite Galois extension of elds with Galois group G, there is a functor c∗ L/k : SHG → SHk from the G-equivariant stable homotopy category to the stable motivic homotopy category over k such that c∗ L/k (G/H+) = Spec(L)+. The main theorem of [7] s...

We use the isomorphism Spin(4) = Spin(3) × Spin(3) to propose a quantization the four-dimensional spin cobordism category away from the prime two, as a Weyl algebra of endomorphisms of the three-dimensional spin cobordism category. 1. The 4D spin cobordism category . . . The classifying spectrum of the (symmetric monoidal) cobordism category with compact oriented d-manifolds as objects, and D =...

Abstract. Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal. Hovey gave a bijection between the set of coherent subcategories of the category of finitely presented R-modules and the set of thick subcategories of the derived category of perfect R-complexes. Using this isomorphism, he proved that every coherent subcategory of finitely presented R-module...

A family of models for category learning is developed, all members being based on a common memory array but differing in memory access and decision processes. Within this framework, fully controlled comparisons of exemplar-similarity, feature-frequency, and prototype models reveal isomorphism between models of different types under some conditions but empirically testable differences under othe...

Homotopy theory studies topological spaces up to homotopy, so it must study the functor π∗ : Top → Π−algebras. Passage to the homotopy category is declaring π∗-isomorphisms to be isomorphisms. Because this functor is difficult to compute, one way to do homotopy theory is to study simpler functors which also map to graded abelian categories, e.g. πQ ∗ , H∗(−;Z), K∗, or more generally E∗ for E so...

The dual of the category of pointed objects of a topos is semiabelian, thus is provided with a notion of semi-direct product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. First, we show this to be equivalent to the existence of initial normal covers in the category of pointed objects of the topos. For Grothendieck toposes...