Semigroups with S.M.F. structures.
Skew-monoidal structures on simple rings with several objects.
Squared Hopf algebras and reconstruction theorems
Given an abelian 𝑉-linear rigid monoidal category 𝑉, where 𝑉 is a perfect field, we define squared coalgebras as objects of cocompleted 𝑉 ⨂ 𝑉 (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If 𝑉 is the category of 𝑉-vector spaces, squared (co)algebras coincide with conventional ones. If 𝑉 is braided, a braided Hopf algebra can be obtained from a squared...
Stack completions and Morita equivalence for categories in a topos
Stacks and equivalence of indexed categories
Symmetric monoidal completions and the exponential principle among labeled combinatorial structures.