7 papers
Enhanced -categories of models of sketches as enhanced -categories of algebras over monads
Joanna Ko
We establish the equivalence between models of enhanced -sketches and algebras over monads, including the (co)lax morphisms. More precisely, for any enhanced limit -sketch $\…
Limits of -categories with structure and their lax morphisms
Joanna Ko
Riehl and Verity have established that for a quasi-category that admits limits, and a homotopy coherent monad on which does not preserve limits, the Eilenberg-Moore object…
Enhanced 2-categorical structures, two-dimensional limit sketches and the symmetry of internalisation
Nathanael Arkor, John Bourke, Joanna Ko
Many structures of interest in two-dimensional category theory have aspects that are inherently strict. This strictness is not a limitation, but rather plays a fundamental role in…
Dotted -limits
Joanna Ko
Marked limits, or Cartesian quasi-limits introduced by Gray, give an alternative approach to -weighted limits in -category theory. This was first established by St…
Existence of groupoid models for diagrams of groupoid correspondences
Joanna Ko, Ralf Meyer
This article continues the study of diagrams in the bicategory of étale groupoid correspondences. We prove that any such diagram has a groupoid model and that the groupoid model is…
Monadic forgetful functors and (non-)presentability for - and -algebras
Alexandru Chirvasitu, Joanna Ko
We prove that the forgetful functors from the categories of - and -algebras to Banach -algebras, Banach algebras or Banach spaces are all monadic, answering a question…
The bicategory of groupoid correspondences
Celso Antunes, Joanna Ko, Ralf Meyer
We define a bicategory with étale, locally compact groupoids as objects and suitable correspondences, that is, spaces with two commuting actions as arrows; the 2-arrows are injecti…