‣ EndAsEqualizer( C, HomC, ForgetfulFunctor, IndexSet ) | ( function ) |
‣ EndByLifts( C, HomC, ForgetfulFunctor, Objects ) | ( function ) |
‣ ReconstructTableOfMarks( C, MinimalGeneratingSet, Decompose ) | ( function ) |
‣ HomSkeletalFinRightGSets( S, T ) | ( function ) |
Returns: a finite set (see FinSetsForCAP)
The finite set \(\mathrm{Hom}_{\mathrm{SkeletalFinGSets}}( S, T )\).
‣ ForgetfulFunctorSkeletalCategoryOfFiniteRightGSets( G ) | ( attribute ) |
Returns: a functor SkeletalFinGSets \(\rightarrow\) SkeletalFinSets
The forgetful functor SkeletalFinGSets \(\rightarrow\) SkeletalFinSets.
‣ ReconstructGroup( C, HomC, ForgetfulFunctor, GeneratingSet, EndImplementation ) | ( function ) |
Returns: a group
The input is a CAP category C which is equivalent to the skeletal category of finite right \(G\)-sets for some group \(G\), a function HomC computing homs in C (e.g. HomSkeletalFinRightGSets), a generating set of C, and a function computing ends (e.g. EndAsEqualizer or EndByLifts). The output is a group isomorphic to \(G\).
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