General associativity and general composition for double categories

In the limit where the wells are far apart and the potential barrier is high, we prove that the ground state and first excited state are given to leading order by an even,

We make this distinction between the superposition principle (with incoherent summing) and a Huygens’ principle (with coherent summing) to make sure that we respect what we can do

The characterisation of double central extensions in terms of commutators due to Janelidze (in the case of groups) and Gran and Rossi (in the case of Mal’tsev varieties) is shown

of a lax double functor S: I —• A defined on a small pseudo double category I can be constructed with the 'basic' double limits in A, considered in Part I: small double

The subcategory of vertical arrows is similarly defined, and these form horizontal domains and codomains of cells.. We will find it useful to

The strict double category Dbl is a crucial, interesting structure where our adjunctions will live; it consists of pseudo double categories, lax and colax

All the (pseudo) double categories considered in Section 3 have tabulators and cotabulators, most of which are calculated in 6.1-5.. called "representable" if

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