subdiagram

A subdiagram is a portion of a diagram that includes a selected set of its objects (nodes) and arrows (morphisms) and inherits the incidence relations from the larger diagram. It is formed by restricting the diagram to a subset of its components while preserving how the components connect.

In category-theoretic terms, a diagram is often described as a functor from an index category to a target category. A subdiagram can be obtained by restricting that functor to a subcategory of the index category, yielding a diagram that traces only the chosen indices. A subdiagram may be described as full if it contains every arrow between the selected objects that appears in the original diagram.

Subdiagrams occur across various mathematical and applied contexts. In graph theory or network diagrams, a subdiagram corresponds to a subgraph that contains some vertices and edges. In commutative diagrams, subdiagrams are used to focus on a portion that still satisfies the same commutativity relations. In circuit diagrams or data-flow diagrams, subdiagrams represent subcircuits or modular components that can be analyzed independently.

Notes and considerations: subdiagrams may or may not preserve all properties of the larger diagram, depending on which arrows are included and how composition or equivalence relations are defined. They are a useful tool for modular reasoning, local analysis, and stepwise construction within complex diagrams.