We develop the theory of relative monads and relative adjunctions in a virtual equipment,
extending the theory of monads and adjunctions in a 2-category. The theory of relative …

Part I of this thesis concerns semi-strictification in low-dimensional higher category theory.
There are many different models of higher dimensional categories, and many differences …

This work studies the proof theory of left (right) skew monoidal closed categories and skew
monoidal bi-closed categories from the perspective of non-associative Lambek calculus …

Monoidal closed categories naturally model NMILL, non-commutative multiplicative
intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and …

We show that the semi-strictly generated internal homs of Gray-categories [A, B] ssg defined
in [20] underlie a closed structure on the category Gray-Cat of Gray-categories and Gray …

In this paper, we develop the proof theory of skew prounital closed categories. These are
variants of the skew closed categories of Street where the unit is not represented. Skew …

The skew monoidal categories of Szlach\'anyi are a weakening of monoidal categories
where the three structural laws of left and right unitality and associativity are not required to …

We explain how to recast the semantics of the simply-typed λ-calculus, and its linear and
ordered variants, using multi-ary structures. We define universal properties for …

The symmetric skew monoidal categories of Bourke and Lack are a weakening of Mac
Lane's symmetric monoidal categories where (i) the three structural laws of left and right …

Let A be a k-algebra over a commutative ring k. By the renowned Tannaka-Kreĭn
reconstruction, liftings of the monoidal structure from M k to MA correspond to bialgebra …