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freeResolution(CpMackeyFunctor,ZZ) -- constructs a free Mackey functor resolution of specified length

Description

This method returns a free resolution of the Mackey functor $M$ up to the $n$th term. The resolution is implemented as a list of Mackey functor homomorphisms.

i1 : M = makeZeroOnUnderlyingMackeyFunctor(3,ZZ^1);
 
i2 : res(M,3)

o2 = {        fix : | 1 0 |       ,         fix : | 0 |           ,    
        1  <-----------------   2                 | 1 |               1
      ZZ                      ZZ      2  <-------------------   1   ZZ 
      ^ |                     ^ |   ZZ                        ZZ    ^ |
      | |                     | |   ^ |                       ^ |   | |
      | v                     | v   | |                       | |   | v
        0  <-----------------   1   | v                       | v     3
      ^ |     und : 0         ZZ      1  <-------------------   3   ZZ 
      └-┘                     ^ |   ZZ      und : | 1 1 1 |   ZZ    ^ |
                              └-┘   ^ |                       ^ |   └-┘
                                    └-┘                       └-┘ 
     ------------------------------------------------------------------------
        fix : 0                  ,         fix : | 3 1 3 |         }
     <----------------------   1     1  <---------------------   3
                             ZZ    ZZ                          ZZ
                             ^ |   ^ |                         ^ | 
                             | |   | |                         | | 
                             | v   | v                         | v 
     <----------------------   3     3  <---------------------   4
        und : | -1 0  1  |   ZZ    ZZ      und : | 1 1 1 1 |   ZZ
              | 1  -1 0  |   ^ |   ^ |           | 1 1 1 1 |   ^ | 
              | 0  1  -1 |   └-┘   └-┘           | 1 1 1 1 |   └-┘ 

o2 : List

Caveat

The optional inputs listed on this page are coming from overloading the resolution method, and don't have any effect on computing resolutions for Mackey functors.

See also

Ways to use this method:

The source of this document is in CpMackeyFunctors/Documentation/ResolutionsDoc.m2:67:0.