Joanna Ko

activity

20242026

collaborators

4 papers

math.CT2026

Enhanced $2$ -categories of models of sketches as enhanced $2$ -categories of algebras over monads

Joanna Ko

We establish the equivalence between models of enhanced $2$ -sketches and algebras over monads, including the (co)lax morphisms. More precisely, for any enhanced limit $2$ -sketch $\…

math.CT2026

Dotted $2$ -limits

Joanna Ko

Marked limits, or Cartesian quasi-limits introduced by Gray, give an alternative approach to $Cat$ -weighted limits in $2$ -category theory. This was first established by St…

math.CT2025

Limits of $(\infty, 1)$ -categories with structure and their lax morphisms

Joanna Ko

Riehl and Verity have established that for a quasi-category $A$ that admits limits, and a homotopy coherent monad on $A$ which does not preserve limits, the Eilenberg-Moore object…

math.CT2024

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…

Enhanced 2-categories of models of sketches as enhanced 2-categories of algebras over monads

Dotted 2-limits

Limits of (∞,1)-categories with structure and their lax morphisms

Enhanced 2-categorical structures, two-dimensional limit sketches and the symmetry of internalisation

Enhanced $2$ -categories of models of sketches as enhanced $2$ -categories of algebras over monads

Dotted $2$ -limits

Limits of $(\infty, 1)$ -categories with structure and their lax morphisms