In this paper, we demonstrated the equivalencies of internal categories
 cat-1 groups and cat-2 structures using some related equivalent
 categories.

Let k be a field. We show that locally presentable, k-linear categories $${\mathcal {C}}$$ dualizable in the sense identity functor can recovered as $$\coprod _i x_i\otimes f_i$$ for objects $$x_i\in {\mathcal and left adjoints $$f_i$$ from to $$\mathrm {Vect}_k$$ are products of copies . This partially confirms conjecture by Brandenburg, author T. Johnson-Freyd. Motivated this, we also charact...

There are two ways to describe the interaction between classical and quantum information categorically: one based on completely positive maps between Frobenius algebras, the other using symmetric monoidal 2-categories. This paper makes a first step towards combining the two. The integrated approach allows a unified description of quantum teleportation and classical encryption in a single 2-cate...