inducedMap(CpMackeyFunctor,CpMackeyFunctor) -- tries to induce a natural map between two Mackey functors

Function: inducedMap
Usage:

inducedMap(N,M)

inducedMap(N,M,F)

inducedMap(N,M,u,f)
Inputs:
- N, a C_p Mackey Functor, target
- M, a C_p Mackey Functor, source
Optional inputs:
- Degree => ..., default value null
- Verify => ..., default value true
Outputs:
- a Mackey Functor homomorphism, a Mackey functor homomorphism from M to N

Description

If a homomorphism is given (either as a MackeyFunctorHomomorphism or as a pair of matrices), this method will try to induce a map between the provided Mackey functors. If no homomorphism is given, the identity morphism on the source is used. A common use for this method to produce the natural inclusion of a subobject or the natural projection to a quotient object.

i1 : f := complexLinearizationMap(3);

i2 : inducedMap(coker f, target f)

o2 =                     fix : | 0 0 0  |
                               | 0 1 -1 |
                               | 0 0 0  |
     cokernel | 1 1 | <--------------------   3
              | 0 1 |                       ZZ
              | 0 1 |                       ^ | 
            ^ |                             | | 
            | |                             | | 
            | v                             | v 
       cokernel | 1 | <--------------------   1
            ^ |          und : 0            ZZ
            └-┘                             ^ | 
                                            └-┘ 

o2 : MackeyFunctorHomomorphism

Ways to use this method:

inducedMap(CpMackeyFunctor,CpMackeyFunctor) -- tries to induce a natural map between two Mackey functors
inducedMap(CpMackeyFunctor,CpMackeyFunctor,MackeyFunctorHomomorphism)
inducedMap(CpMackeyFunctor,CpMackeyFunctor,Matrix,Matrix)

The source of this document is in CpMackeyFunctors/Documentation/HomomorphismsDoc.m2:352:0.

inducedMap(CpMackeyFunctor,CpMackeyFunctor) -- tries to induce a natural map between two Mackey functors

Description

See also

Ways to use this method: