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# 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

## See also

- Making chain complexes -- information about the basic constructors
- Making maps between chain complexes -- information about the basic constructors
- Basic invariants and properties -- information about accessing basic features
- Working with Tor -- information about functorial properties
- Towards computing in the derived category

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Complexes/ChainComplexDoc.m2:201:0.