SimplicialModuleMap -- the class of all maps between simplicial modules

Description

A map of simplicial modules $f \colon C \rightarrow D$ of degree $d$ is a sequence of maps $f_i \colon C_i \rightarrow D_{d+i}$. No relationship between the maps $f_i$ and the face/degeneracy maps of either $C$ or $D$ is assumed. If a simplicial module map is obtained as the image of a morphism of complexes under the Dold-Kan functor, the key complexMap will be stored for more efficient normalization computations.

The usual algebraic operations are available: addition, subtraction, scalar multiplication, and composition. The identity map from a simplicial module to itself can be produced with id. An attempt to add (subtract, or compare) a ring element to a simplicial module map will result in the ring element being multiplied by the appropriate identity map.

Functions and methods returning a Map of Simplicial Modules:

Number + SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
Number - SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
RingElement + SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
RingElement - SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap + Number -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap + RingElement -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap - Number -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap - RingElement -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap - SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
basis(List,SimplicialModuleMap) (missing documentation)
basis(ZZ,SimplicialModuleMap) (missing documentation)
extPower(ZZ,SimplicialModuleMap) -- see extPower -- compute the Dold-Puppe extension of the exterior power functor to simplicial modules
Symbol ^ SimplicialModule -- see face/degeneracy maps of a simplicial module -- access the face and degeneracy maps of a simplicial module
HH SimplicialModuleMap (missing documentation)
inducedMap(SimplicialModule,SimplicialModule) -- make the map of simplicial modules induced at each term by the identity map
map(SimplicialModule,SimplicialModule,HashTable) -- make a map of simplicial modules
map(SimplicialModule,SimplicialModule,SimplicialModuleMap) -- make a new map of simplicial modules, induced from an existing one
map(SimplicialModule,SimplicialModule,ZZ) -- make the zero map or identity between simplicial modules
minimalPresentation(SimplicialModuleMap) -- see minimalPresentation(SimplicialModule) -- minimal presentation of all terms in a simplicial module
prune(SimplicialModuleMap) -- see minimalPresentation(SimplicialModule) -- minimal presentation of all terms in a simplicial module
randomSimplicialMap(SimplicialModule,SimplicialModule) -- a random map of simplicial modules
Ring ** SimplicialModuleMap -- see RingMap ** SimplicialModuleMap -- tensor a map of simplicial modules along a ring map
RingMap ** SimplicialModuleMap -- tensor a map of simplicial modules along a ring map
SimplicialModuleMap ** Ring -- see RingMap ** SimplicialModuleMap -- tensor a map of simplicial modules along a ring map
SimplicialModuleMap ** RingMap -- see RingMap ** SimplicialModuleMap -- tensor a map of simplicial modules along a ring map
tensor(RingMap,SimplicialModuleMap) -- see RingMap ** SimplicialModuleMap -- tensor a map of simplicial modules along a ring map
tensor(SimplicialModuleMap,RingMap) -- see RingMap ** SimplicialModuleMap -- tensor a map of simplicial modules along a ring map
RingMap SimplicialModuleMap -- apply a ring map to a map of simplicial modules
schurMap(List,SimplicialModuleMap) -- see schurMap -- construct the Dold-Puppe extension of the Schur functor
Matrix ** SimplicialModule -- see SimplicialModule ** Matrix -- create the tensor product of a simplicial module and a map of modules
SimplicialModule ** Matrix -- create the tensor product of a simplicial module and a map of modules
SimplicialModule ^ Array -- see SimplicialModule _ Array -- the canonical inclusion or projection map of a direct sum
SimplicialModule _ Array -- the canonical inclusion or projection map of a direct sum
simplicialModule(ComplexMap) (missing documentation)
simplicialModule(ComplexMap,ZZ) (missing documentation)
Complex ** SimplicialModuleMap -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
ComplexMap ** SimplicialModuleMap -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
Module ** SimplicialModuleMap -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
SimplicialModule ** SimplicialModuleMap -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
SimplicialModuleMap ** Complex -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
SimplicialModuleMap ** ComplexMap -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
SimplicialModuleMap ** Module -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
SimplicialModuleMap ** SimplicialModule -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
tensor(SimplicialModuleMap,SimplicialModuleMap) -- see SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
SimplicialModuleMap ++ SimplicialModuleMap -- direct sum of simplicial module maps
SimplicialModuleMap ^ Array -- the composition with the canonical inclusion or projection map
SimplicialModuleMap _ Array -- see SimplicialModuleMap ^ Array -- the composition with the canonical inclusion or projection map
SimplicialModuleMap ^ ZZ -- the n-fold composition
SimplicialModuleMap | SimplicialModuleMap -- join or concatenate maps horizontally
SimplicialModuleMap || SimplicialModuleMap -- join or concatenate maps vertically
truncate(List,SimplicialModuleMap) -- truncation of a simplicial module map at a specified degree or set of degrees
truncate(ZZ,SimplicialModuleMap) -- see truncate(List,SimplicialModuleMap) -- truncation of a simplicial module map at a specified degree or set of degrees

Methods that use a Map of Simplicial Modules:

- SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
Number * SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
RingElement * SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap * Number -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap * RingElement -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
SimplicialModuleMap + SimplicialModuleMap -- see arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
coimage(SimplicialModuleMap) -- make the coimage of a map of simplicial modules
cokernel(SimplicialModuleMap) -- make the cokernel of a map of simplicial modules
components(SimplicialModuleMap) -- list the components of a direct sum
degree(SimplicialModuleMap) -- get the degree of a map of simplicial modules
expression(SimplicialModuleMap) (missing documentation)
image(SimplicialModuleMap) -- make the image of a map of simplicial modules
isCommutative(SimplicialModuleMap) -- whether a simplicial module map commutes with the face/degeneracy maps
isHomogeneous(SimplicialModuleMap) -- whether a map of simplicial modules is homogeneous
isShortExactSequence(SimplicialModuleMap,SimplicialModuleMap) -- whether a pair of simplicial module maps forms a short exact sequence
isSimplicialMorphism(SimplicialModuleMap) -- whether a simplicial module map is a morphism of simplicial modules
isWellDefined(SimplicialModuleMap) -- whether a map of simplicial modules is well-defined
kernel(SimplicialModuleMap) -- make the kernel of a map of simplicial modules
net(SimplicialModuleMap) (missing documentation)
normalize(SimplicialModuleMap) -- see normalize(SimplicialModule,ZZ) -- normalization functor from simplicial modules to nonnegatively-graded chain complexes
normalize(SimplicialModuleMap,ZZ) -- see normalize(SimplicialModule,ZZ) -- normalization functor from simplicial modules to nonnegatively-graded chain complexes
ring(SimplicialModuleMap) -- see ring(SimplicialModule) -- access the ring of a simplicial module or a simplicial module map
SimplicialModuleMap Array -- see SimplicialModule Array -- shift a simplicial module or simplicial module map
SimplicialModuleMap * SimplicialModuleMap -- composition of homomorphisms of simplicial modules
directSum(SimplicialModuleMap) -- see SimplicialModuleMap ++ SimplicialModuleMap -- direct sum of simplicial module maps
SimplicialModuleMap == SimplicialModuleMap -- whether two simplicial module maps are equal
SimplicialModuleMap == ZZ -- see SimplicialModuleMap == SimplicialModuleMap -- whether two simplicial module maps are equal
ZZ == SimplicialModuleMap -- see SimplicialModuleMap == SimplicialModuleMap -- whether two simplicial module maps are equal
SimplicialModuleMap _ Sequence -- see SimplicialModuleMap _ ZZ -- access individual matrices in a simplicial module map
SimplicialModuleMap _ ZZ -- access individual matrices in a simplicial module map
source(SimplicialModuleMap) -- get the source of a map of simplicial modules
target(SimplicialModuleMap) -- get the target of a map of simplicial modules
topDegree(SimplicialModuleMap) -- see topDegree -- top degree of a simplicial module

For the programmer

The object SimplicialModuleMap is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:1356:0.

SimplicialModuleMap -- the class of all maps between simplicial modules

Description

See also

Functions and methods returning a Map of Simplicial Modules:

Methods that use a Map of Simplicial Modules:

For the programmer