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math.CT2026
A duality between monads and monadic morphisms
Hadrian Heine
We establish a duality between monads and monadic morphisms in any -category and characterize monadic morphisms in a wide class of examples. This duality unifies severa…
math.CT2025
On bi-enriched -categories
Hadrian Heine
We extend Lurie's definition of enriched -categories to notions of left enriched, right enriched and bienriched -categories, which generalize the concepts of closed…
math.CT2024
The higher algebra of weighted colimits
Hadrian Heine
We develop a theory of weighted colimits in the framework of weakly bienriched -categories, an extension of Lurie's notion of enriched -categories. We prove an exis…