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4 papers · 2 filters
Internal lenses as functors and cofunctors
Bryce Clarke
Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Wo…
Adjoint functor theorems for homotopically enriched categories
John Bourke, Stephen Lack, Lukáš Vokřínek
We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category admitting certain limits. When is equipped with the…
Freely adjoining monoidal duals
Kevin Coulembier, Ross Street, Michel van den Bergh
Given a monoidal category with an object , we construct a monoidal category by freely adjoining a right dual to . We show tha…
The Gray tensor product for 2-quasi-categories
Yuki Maehara
We construct an -version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an -ary) functor on the category of -…