nLab extension (double category theory)

Idea

The notion of extensions in a double category abstracts that of the classical operation of extension of scalars of bimodules. Indeed, they are usually available in framed bicategories, which are formal analogues to double categories of bimodules; and indeed extensions in a double category of bimodules correspond to extensions of scalars.

The dual notion is that of restriction. Since having all restrictions is equivalent to having all extensions, and since in double category theory one usually works with the former, we redirect the reader to the aforementioned page.

Related concepts

• restriction (double category theory)

References

• Mike Shulman, Framed bicategories and monoidal fibrations, Theory and Applications of Categories 20 18 (2008) 650–738 [tac:2018, arXiv:0706.1286]