204 Citations
J an 2 01 7 On the notion of flat 2-functors
- Mathematics
- 2017
In this paper we develop the 2-dimensional theory of flat functors. We define a 2-functor A P −→ Cat to be flat when its left bi-Kan extension Homp(A , Cat) P∗ −→ Cat along the Yoneda 2-functor A h…
Familial 2-functors and parametric right adjoints
- Mathematics
- 2007
We define and study familial 2-functors primarily with a view to the devel- opment of the 2-categorical approach to operads of (Weber, 2005). Also included in this paper is a result in which the…
A Trace for Bimodule Categories
- MathematicsAppl. Categorical Struct.
- 2017
A 2-functor that assigns to a bimodule category over a finite tensor category a 𝕜$\Bbbk $-linear abelian category has coherent cyclic invariance and has applications to categories associated to circles in three-dimensional topological field theories with defects.
The Three F's for Bicategories I: Localization by Fractions is Exact
- Mathematics
- 2021
We study the interaction between the notions of filteredness, fractions and fibrations in the theory of bicategories, generalizing classical results for categories. We give an explicit formula for…
Coherent Presentations of Monoidal Categories
- MathematicsLog. Methods Comput. Sci.
- 2017
It is shown that, under suitable coherence conditions on the presentation, the three constructions coincide, thus generalizing celebrated results on presentations of groups, and extending those conditions to presentations of monoidal categories.
A general limit lifting theorem for 2-dimensional monad theory
- MathematicsJournal of Pure and Applied Algebra
- 2018
Weighted limits in an (∞ , 1)-category
- MathematicsAppl. Categorical Struct.
- 2021
The notion of weighted limit in an arbitrary quasi-category is introduced, suitably generalizing ordinary limits in a quasi- category, and classical weighted limits in an ordinary category by generalizing Joyal's approach.
References
SHOWING 1-10 OF 13 REFERENCES
A notion of limit for enriched categories
- MathematicsBulletin of the Australian Mathematical Society
- 1975
For a V-category B, where V is a symmetric monoidal closed category, various limit-like notions have been recognized: ordinary limits (in the underlying category B0 ) preserved by the V-valued…
Formal category theory: adjointness for 2-categories
- Mathematics, Philosophy
- 1974
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.
Adjonctions et monades au niveau des 2-catégories
- Mathematics
- 1974
© Andrée C. Ehresmann et les auteurs, 1974, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les…