Working with simplicial maps -- information about simplicial maps and the induced operations

Let $C$ and $D$ be simplicial complexes. A simplicial map is a map $f : C \to D$ such that for any face $F \subset C$, we have that $f(F)$ is contained in a face of $D$.

Although the primary method for creating a simplicial map is map(SimplicialComplex,SimplicialComplex,Matrix), there are a few other constructors.

Making simplicial maps

• map(SimplicialComplex,SimplicialComplex,Matrix) -- create a simplicial map between simplicial complexes
• id _ SimplicialComplex -- make the identity map from a SimplicialComplex to itself
• SimplicialMap -- the class of all maps between simplicial complexes
• isWellDefined(SimplicialMap) -- whether underlying data is uncontradictory

Having made a simplicial map, one can access its basic invariants or test for some elementary properties by using the following methods. Having made a map of abstract simplicial complexes, one can access its basic invariants or test for some elementary properties by using the following methods.

Determining attributes and properties of simplicial maps

• source(SimplicialMap) -- get the source of the map
• target(SimplicialMap) -- get the target of the map
• matrix(SimplicialMap) -- get the underlying map of rings