  We present the proof assistant homotopy.io for working with
finitely-presented semistrict higher categories. The tool runs in the browser
with a point-and-click interface, allowing direct manipulation of proof objects
via a graphical representation. We describe the user interface and explain how
the tool can be used in practice. We also describe the essential subsystems of
the tool, including collapse, contraction, expansion, typechecking, and layout,
as well as key implementation details including data structure encoding,
memoisation, and rendering. These technical innovations have been essential for
achieving good performance in a resource-constrained setting.
