• Corpus ID: 117077641

Fibrations of predicates and bicategories of relations

  title={Fibrations of predicates and bicategories of relations},
  author={Finn Lawler},
  journal={arXiv: Category Theory},
  • F. Lawler
  • Published 27 February 2015
  • Mathematics
  • arXiv: Category Theory
We reconcile the two different category-theoretic semantics of regular theories in predicate logic. A 2-category of `regular fibrations' is constructed, as well as a 2-category of `regular proarrow equipments', and it is shown that the two are equivalent. A regular equipment is a `cartesian equipment' satisfying certain axioms, and a cartesian equipment is a slight generalization of a cartesian bicategory. This is done by defining a tricategory Biprof whose objects are bicategories and whose… 
4 Citations

Figures from this paper

Day convolution for monoidal bicategories
Ends and coends can be described as objects which are universal amongst extranatural transformations. We describe a cate- gorification of this idea, extrapseudonatural transformations, in such a
Knowledge Representation in Bicategories of Relations
This paper shows by example that relational ologs have a friendly and intuitive--yet fully precise--graphical syntax, derived from the string diagrams of monoidal categories, and explains several other useful features of relational o logics not possessed by most description logics, such as a type system and a rich, flexible notion of instance data.
Computing Weighted Colimits
A well-known result of SGA4 shows how to compute the pseudo-colimit of a category-valued pseudo-functor on a 1-category. The main result of this paper gives a generalization of this computation by
A universal characterisation of codescent objects
In this work we define a 2-dimensional analogue of extranatural transformation and use these to characterise codescent objects. They will be seen as universal objects amongst pseudo-extranatural


Framed bicategories and monoidal fibrations
In some bicategories, the 1-cells are `morphisms' between the 0-cells, such as functors between categories, but in others they are `objects' over the 0-cells, such as bimodules, spans, distributors,
Maps II: Chasing Diagrams in Categorical Proof Theory
This paper investigates proof theory of regular logic the {A,3}-fragment of the first order logic with equality, and determines precise conditions under which a regular fibration supports the principle of function comprehension, thus lifting a basic theorem from regular categories.
A $2$-categorical approach to change of base and geometric morphisms I
We introduce a notion of equipment which generalizes the earlier notion of pro-arrow equipment and includes such familiar constructs as relK, spnK, parK ,a nd proK for a suitable category K, along
Coherent extensions and relational algebras
ABSTRACT. The notion of a lax adjoint to a 2-functor is introduced and some aspects of it are investigated, such as an equivalent definition and a corresponding theory of monads. This notion is
Enhanced 2-categories and limits for lax morphisms
Abstract We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or
A category may bear many monoidal structures, but (to within a unique isomorphism) only one structure of "category with finite products". To capture such distinctions, we consider on a 2-category
Limits indexed by category-valued 2-functors
There is common agreement now on the correct general notion of limit for categories whose horns are enriched in a suitable category 13. The definition involves a v-functor J: A + v which should be
Enriched categories as a free cocompletion
Abstract This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory—categorifying the classical theory of categories enriched in a monoidal
All realizability is relative
We introduce a category of basic combinatorial objects, encompassing PCAs and locales. Such a basic combinatorial object is to be thought of as a pre-realizability notion. To each such object we can
The formal theory of monads II
Abstract We give an explicit description of the free completion EM ( K ) of a 2-category K under the Eilenberg–Moore construction, and show that this has the same underlying category as the