Working with Ext -- information about functorial properties

Hom and Ext

• Ext^ZZ(Module,Module) -- Ext module
• Ext^ZZ(Matrix,Module) -- map between Ext modules
• Ext^ZZ(Module,Matrix) -- map between Ext modules
• Ext(Module,Module) -- total Ext module
• Hom(Complex,Complex) -- the complex of homomorphisms between two complexes
• Hom(ComplexMap,ComplexMap) -- the map of complexes between Hom complexes
• homomorphism(ComplexMap) -- get the homomorphism from an element of Hom
• homomorphism'(ComplexMap) -- get the element of Hom from a map of complexes
• connectingExtMap(Module,Matrix,Matrix) -- makes the connecting maps in Ext

Yoneda extensions and elements of Ext

• yonedaMap(Matrix) -- creates a chain complex map representing an extension of modules
• yonedaMap'(ComplexMap) -- identifies the element of Ext corresponding to a map of free resolutions
• yonedaExtension(Matrix) -- creates a chain complex representing an extension of modules
• yonedaExtension'(Complex) -- identifies the element of Ext corresponding to an extension
• yonedaProduct(Matrix,Matrix) -- make the product of two elements in Ext modules
• yonedaProduct(Module,Module) -- make the product map between Ext modules