Quasi-Kan extensions for 2-categories

  title={Quasi-Kan extensions for 2-categories},
  author={J. Gray},
  journal={Bulletin of the American Mathematical Society},
  • J. Gray
  • Published 1974
  • Mathematics
  • Bulletin of the American Mathematical Society
Pseudo-Kan Extensions and Descent Theory
There are two main constructions in classical descent theory: the category of algebras and the descent category, which are known to be examples of weighted bilimits. We give a formal approach toExpand
We prove a biadjoint triangle theorem and its strict version, which are 2-dimensional analogues of the adjoint triangle theorem of Dubuc. Similarly to the 1-dimensional case, we demonstrate how weExpand
An Australian Conspectus of Higher Categories
Much Australian work on categories is part of, or relevant to, the development of higher categories and their theory. In this note, I hope to describe some of the origins and achievements of ourExpand
C T ] 6 J ul 2 00 0 Coherence , Homotopy and 2-Theories
2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central toExpand
Pseudo Limits, Biadjoints, and Pseudo Algebras: Categorical Foundations of Conformal Field Theory
Introduction Some comments on conformal field theory Weighted pseudo limits in a 2-category Weighted pseudo colimits in the 2-category of small categories Weighted pseudo limits in the 2-category ofExpand
Coherence, Homotopy and 2-Theories
Theories are a canonical way of describing categories with extra struc- ture. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central toExpand
1 O ct 1 99 9 The Syntax of Coherence
This article tackles categorical coherence within a two-dimensional generalization of Lawvere’s functorial semantics. 2-theories, a syntactical way of describing categories with structure, areExpand
The syntax of coherence
Cet article etudie la coherence categorique dans le cadre d'une generalisation 2-dimensionnelle de la semantique fonctorielle de Lawvere. On y presente les 2-theories, maniere syntactique de decrireExpand


Closed categories, Proc
  • Conf. Categorical Algebra (La Jolla, Calif., 1965), Springer, New York, 1966, pp. 421-562. MR 37 #1432.
  • 1974
Formal category theory: adjointness for 2-categories
Categories.- 2-categories.- Bicategories.- Properties of Fun(A,B) and Pseud(A,B).- Properties of 2-comma categories.- Adjoint morphisms in 2-categories.- Quasi-adjointness.
Topos annelés et schémas relatifs
Bifibration induced adjoint pairs
Cohomologie non abélienne
The categorical comprehension scheme
The categorical comprehension scheme, Category Theory, Homology Theory and their Applications, III (Battelle
  • Lecture Notes in Math.,
  • 1969
Reports of the Midwest Category Seminar I
Hopf and Eilenberg-Maclane algebras.- Discoherently associative bifunctors on groups.- Directed colimits and sheaves in some non-abelian categories.- Bifibration induced adjoint pairs.- The doubleExpand
Fibred and Cofibred Categories
Fibred categories were introduced by Gkothendieck in [SGA] and [BB190]. As far as I know these are the only easily available references to the subject. Through sheer luck, during the finalExpand