Each full reflective subcategory X of a finitely-complete category C gives rise to a factorization system (E,M) on C, where E consists of the morphisms of C inverted by the reflexion I : C → X . Under a simplifying assumption which is satisfied in many practical examples, a morphism f : A → B lies in M precisely when it is the pullback along the unit ηB : B → IB of its reflexion If : IA → IB; w...

in this paper we construct the category of coverings of fundamental generalized lie group-groupoid associatedwith a connected generalized lie group. we show that this category is equivalent to the category of coverings of aconnected generalized lie group. in addition, we prove the category of coverings of generalized lie groupgroupoidand the category of actions of this generalized lie group-gro...

This paper is an expanded version of my lecture delivered at the 97 Seattle summer research conference on finite fields. It gives a quick exposition of Dwork’s conjecture about p-adic meromorphic continuation of his unit root L-function arising from a family of algebraic varieties defined over a finite field of characteristic p. As a simple illustration, we discuss the classical example of the ...

in a previous paper, the second author established that, given finite fields $f < e$ and certain subgroups $c leq e^times$, there is a galois connection between the intermediate field lattice ${l mid f leq l leq e}$ and $c$'s subgroup lattice. based on the galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $c rtimes {rm gal} (e/f)$...

A generalised Paley map is a Cayley map for the additive group of a finite field F , with a subgroup S = −S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the orientably regular maps with orientation-preserving automorphism group acting primitively and faithfully on the vertices; allowing a non-faithful primitive action ...

Let (N, g) be a closed Riemannian manifold of dimension 2m − 1 and let 0→ Ñ → N be a Galois covering of N . We assume that 0 is of polynomial growth with respect to a word metric and that 1Ñ is L 2-invertible in degree m. By employing spectral sections with a symmetry property with respect to the ?-Hodge operator, we define the higher eta invariant associated with the signature operator on Ñ , ...

Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. In consequence, the fundamental group ir(X, Xo) which we obtain frequently reflects local properties which are missed by the usual arcwise group iri(X, Xo). We obtain a perfect Galois theory of covering...

this paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical galois theory and involves generalized central extensions, commutators, and internal groupoids in barr exact mal’tsev and more general categories. galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...