Category Theory Diagram Commutativity Checker
Category Theory Diagram Commutativity Checker verifies if a categorical diagram commutes by checking if compositions of morphisms along specified paths are equal. Enter objects, morphisms, and paths to compare.
Commutativity in Category Theory
A diagram in a category commutes if, for any two objects, all possible paths of morphisms between them yield the same result under composition. For example, given morphisms \\( f: A \to B \\), \\( g: B \to C \\), and \\( h: A \to C \\), the diagram commutes if:
\\[
g \circ f = h
\\]
Where:
- \\( \circ \\): Denotes morphism composition (apply right morphism first).
- Paths are specified as sequences of morphisms (e.g., \\( f;g \\) means \\( g \circ f \\)).
- The checker verifies if compositions of paths between the same objects are equal.