Corpus ID: 16142961


  author={John Kennison and Robert Raphael},
We develop in some generality the dualities that often arise when one object lies in two different categories. In our examples, one category is equational and the other consists of the topological objects in a (generally different) equational category. 
Stone Dualities from Opfibrations
An abstract notion of formal spaces is defined, and the aim of this paper is to construct fundamental adjunctions generically using (co)fibered category theory. Expand
A General duality Theory for Clones
  • S. Kerkhoff
  • Mathematics, Computer Science
  • Int. J. Algebra Comput.
  • 2013
A general duality theory for clones is outlined that will allow us to dualize any given clone, together with its relational counterpart and the relationship between them. Expand
General affine adjunctions, Nullstellensätze, and dualities
We introduce and investigate a category-theoretic abstraction of the standard "system-solution" adjunction in affine algebraic geometry. We then look further into these geometric adjunctions atExpand
Concrete Dualities and Essential Arities
  • S. Kerkhoff
  • Mathematics, Computer Science
  • 2014 IEEE 44th International Symposium on Multiple-Valued Logic
  • 2014
This paper shows that, under some mild assumptions, the essential arity of finitary operations from an object A to a finite object B in one category is bounded if and only if the concrete form of the copowers of the dual of A has a certain (easily verifiable) set-theoretic property. Expand
Categories of scientific theories
We discuss ways in which category theory might be useful in philosophy of science, in particular for articulating the structure of scientific theories. We argue, moreover, that a categorical approachExpand
Meaning and duality : from categorical logic to quantum physics
Categorical universal logic is developed on the basis of Lawvere’s hyperdoctrine and Hyland-Johnstone-Pitts’ tripos, thereby expanding the realm of (first-order/higher-order) categorical logic so as to encompass, inter alia, classical, intuitionistic, quantum, fuzzy, relevant, and linear logics. Expand
Towards An Approach to Hilbert's Sixth Problem: A Brief Review
In 1900 David Hilbert published his famous list of 23 problems. The sixth of them-the axiomatization of Physics-remains partially unsolved. In this work we will give a gentle introduction and a briefExpand
Exceptional Generalized Geometry, Topological p-branes and Wess-Zumino-Witten Terms
We study the interplay between the AKSZ construction of σ-models, the Hamiltonian formalism in the language of symplectic dg-geometry, the encoding of dynamics and symmetries inside algebroidExpand
Rekonstrukcijski teoremi i spektri
U ovom radu dan je pregled nekih važnih rekonstrukcijskih teorema, odnosno, teorema koji daju vezu između dva objekta na nacin da je jedan objekt m
Isbell conjugacy and the reflexive completion
The reflexive completion of a category consists of the Set-valued functors on it that are canonically isomorphic to their double conjugate. After reviewing both this construction and Isbell conjugacyExpand


A generalization of the duality compactness theorem
Abstract In this article we extend the theory of natural dualities for finitary quasivarieties to model categories of finitary limit sketches.
Algebraic Topology
The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.
A general Stone-Gel’fand duality
We give a simple characterization of full subcategories of equational categories. If d is one such and B is the category of topological spaces, we consider a pair of adjoint functors d0P r S whichExpand
Natural dualities for structures
Following on from results of Hofmann [27], we investigate the extension of the theory of natural dualities to quasivarieties generated by finite structures that can have operations, partialExpand
Groups of dualities
For arbitrary categories si and 38 , the "set" of isomorphism- classes of dualities between si and 3S carries a natural group structure. In case si and 3e admit faithful representable functors toExpand
Structure of categories
Introduction. This paper sets out to develop a structure theory of categories and carries it, not very far, but far enough for some applications. We need a new definition of complete (coinciding withExpand
Toposes, Triples and Theories
1. Categories.- 2. Toposes.- 3. Triples.- 4. Theories.- 5. Properties of Toposes.- 6. Permanence Properties of Toposes.- 7. Representation Theorems.- 8. Cocone Theories.- 9. More on Triples.- IndexExpand
Compact and hypercomplete categories
The paper deals with compact c&ego&s (cf. Isbell [17]), i.e. categories d which have the property that any functor U : d + 9 preserving all existing colimits of Sp has a right adjoint, and withExpand
N-compact frames
We investigate notions of N-compactness for frames. We find that the analogues of equivalent conditions defining N-compact spaces are no longer equivalent in the frame context. Indeed, the closedExpand
) , N - compact frames , Comment
  • 1991