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boxProduct(MackeyFunctorHomomorphism,CpMackeyFunctor) -- induced maps on box products

Description

A map $F\colon P\to Q$ of Mackey functors can be tesnored with a Mackey functor $M$ to form a map $M ⊠ F\colon M ⊠ P\to M ⊠ Q$.

i1 : boxProduct(makeUnderlyingFreeMackeyFunctor(3),complexLinearizationMap(3))

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

o1 : MackeyFunctorHomomorphism

See also

Ways to use this method:

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CpMackeyFunctors/Documentation/BoxProductDoc.m2:73:0.