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math.CT2023
On the tensor product of enriched -categories
Rune Haugseng
We show that the tensor product of -categories enriched in a suitable monoidal -category preserves colimits in each variable, fixing a mistake in an earlier paper o…
math.CT2020
On (co)ends in -categories
Rune Haugseng
In this short note we prove that two definitions of (co)ends in -categories, via twisted arrow -categories and via -categories of simplices, are equivalent.…
math.CT2020
On lax transformations, adjunctions, and monads in -categories
Rune Haugseng
We use the basic expected properties of the Gray tensor product of -categories to study (co)lax natural transformations. Using results of Riehl-Verity and Zaganidis we…