A homeomorphism from a local neighborhood around a point on a topological n-manifold in a Banach space to an n-dimensional Banach space (typically a subspace of the space the manifold is embedded in).
A functor from an index category to another category. The objects and morphisms of the index category need not have any internal substance, but rather merely outline the connective structure of at least some part of the diagram's codomain. If the index category is J and the codomain is C, then the diagram is said to be "of type J in C".
A plan, drawing, sketch or outline to show how something works, or show the relationships between the parts of a whole.
Electrical diagrams show device interconnections.
A graph or chart.
To schedule the operations of a locomotive or train according to a diagram.
To represent or indicate something using a diagram.