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# internalHom(CpMackeyFunctor,MackeyFunctorHomomorphism) -- returns the induced map on an internal hom.

- Function: internalHom
- Usage:
    `internalHom(F,M)`
    `internalHom(M,F)`
- Inputs:
  - M, a C_p Mackey Functor,
  - F, a Mackey Functor homomorphism,
- Outputs:
  - a Mackey Functor homomorphism, the induced map on internal hom Mackey functors

## Description

The internal hom of Mackey functors is functorial in each variable. This method returns the induced maps.

    i1 : prune internalHom(makeRealRepresentationMackeyFunctor(3), complexLinearizationMap(3))

    o1 =         fix : | 1  -2 |
                       | -1 0  |
                       | 0  1  |
           3  <-------------------   2
         ZZ                        ZZ
         ^ |                       ^ |
         | |                       | |
         | v                       | v
           1  <-------------------   1
         ZZ      und : | 1 |       ZZ
         ^ |                       ^ |
         └-┘                       └-┘

    o1 : MackeyFunctorHomomorphism

## See also

- the abelian category of Mackey functors -- background on the category of Mackey functors and how to code within it
- internalHom -- returns the internal hom Mackey functor between two Mackey functors.

## Ways to use this method:

- internalHom(CpMackeyFunctor,MackeyFunctorHomomorphism) -- returns the induced map on an internal hom.
- `internalHom(MackeyFunctorHomomorphism,CpMackeyFunctor)`

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CpMackeyFunctors/Documentation/InternalHomDoc.m2:51:0.