  
  [1X1 [33X[0;0YCAP Categories[133X[101X
  
  [33X[0;0YCategories  are  the main GAP objects in CAP. They are used to associate GAP
  objects  which  represent  objects  and  morphisms  with  their category. By
  associating  a  GAP  object to the category, one of two filters belonging to
  the category (ObjectFilter/MorphismFilter) are set to true. Via Add methods,
  functions  for  specific  existential  quantifiers  can be associated to the
  category and after that can be applied to GAP objects in the category. A GAP
  category  object  also  knows  which constructions are currently possible in
  this category.[133X
  
  
  [1X1.1 [33X[0;0YCategories[133X[101X
  
  [1X1.1-1 IsCapCategory[101X
  
  [29X[2XIsCapCategory[102X( [3Xobject[103X ) [32X filter
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe  GAP  category  of  CAP  categories. Objects of this type handle the CAP
  category  information,  the  caching,  and  filters  for  objects in the CAP
  category.  Please note that the object itself is not related to methods, you
  only need it as a handler and a presentation of the CAP category.[133X
  
  [1X1.1-2 IsCapCategoryCell[101X
  
  [29X[2XIsCapCategoryCell[102X( [3Xobject[103X ) [32X filter
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe  GAP  category of CAP category cells. Every object, morphism, and [23X2[123X-cell
  of a CAP category lies in this GAP category.[133X
  
  [1X1.1-3 IsCapCategoryObject[101X
  
  [29X[2XIsCapCategoryObject[102X( [3Xobject[103X ) [32X filter
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe  GAP  category  of  CAP category objects. Every object of a CAP category
  lies in this GAP category.[133X
  
  [1X1.1-4 IsCapCategoryMorphism[101X
  
  [29X[2XIsCapCategoryMorphism[102X( [3Xobject[103X ) [32X filter
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe GAP category of CAP category morphisms. Every morphism of a CAP category
  lies in this GAP category.[133X
  
  [1X1.1-5 IsCapCategoryTwoCell[101X
  
  [29X[2XIsCapCategoryTwoCell[102X( [3Xobject[103X ) [32X filter
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe  GAP  category  of  CAP category [23X2[123X-cells. Every [23X2[123X-cell of a CAP category
  lies in this GAP category.[133X
  
  
  [1X1.2 [33X[0;0YConstructor[133X[101X
  
  [1X1.2-1 CreateCapCategory[101X
  
  [29X[2XCreateCapCategory[102X(  ) [32X operation
  [6XReturns:[106X  [33X[0;10Ya category[133X
  
  [33X[0;0YCreates a new CAP category from scratch. It gets a generic name.[133X
  
  [1X1.2-2 CreateCapCategory[101X
  
  [29X[2XCreateCapCategory[102X( [3Xs[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Ya category[133X
  
  [33X[0;0YThe  argument  is a string [23Xs[123X. This operation creates a new CAP category from
  scratch. Its name is set to [23Xs[123X.[133X
  
  
  [1X1.3 [33X[0;0YInternal Attributes[133X[101X
  
  [33X[0;0YEach  category  [23XC[123X  stores  various filters. They are used to apply the right
  functions in the method selection.[133X
  
  [1X1.3-1 CategoryFilter[101X
  
  [29X[2XCategoryFilter[102X( [3XC[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya filter[133X
  
  [33X[0;0YThe argument is a cateogry [23XC[123X. The output is a filter in which [23XC[123X lies.[133X
  
  [1X1.3-2 CellFilter[101X
  
  [29X[2XCellFilter[102X( [3XC[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya filter[133X
  
  [33X[0;0YThe argument is a cateogry [23XC[123X. The output is a filter in which all cells of [23XC[123X
  shall lie.[133X
  
  [1X1.3-3 ObjectFilter[101X
  
  [29X[2XObjectFilter[102X( [3XC[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya filter[133X
  
  [33X[0;0YThe argument is a cateogry [23XC[123X. The output is a filter in which all objects of
  [23XC[123X shall lie.[133X
  
  [1X1.3-4 MorphismFilter[101X
  
  [29X[2XMorphismFilter[102X( [3XC[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya filter[133X
  
  [33X[0;0YThe  argument is a cateogry [23XC[123X. The output is a filter in which all morphisms
  of [23XC[123X shall lie.[133X
  
  [1X1.3-5 TwoCellFilter[101X
  
  [29X[2XTwoCellFilter[102X( [3XC[103X ) [32X attribute
  [6XReturns:[106X  [33X[0;10Ya filter[133X
  
  [33X[0;0YThe argument is a cateogry [23XC[123X. The output is a filter in which all [23X2[123X-cells of
  [23XC[123X shall lie.[133X
  
  
  [1X1.4 [33X[0;0YLogic switcher[133X[101X
  
  [1X1.4-1 CapCategorySwitchLogicOn[101X
  
  [29X[2XCapCategorySwitchLogicOn[102X( [3XC[103X ) [32X function
  
  [33X[0;0YActivates the predicate implication logic for the category [3XC[103X.[133X
  
  [1X1.4-2 CapCategorySwitchLogicOff[101X
  
  [29X[2XCapCategorySwitchLogicOff[102X( [3XC[103X ) [32X function
  
  [33X[0;0YDeactivates the predicate implication logic for the category [3XC[103X.[133X
  
  
  [1X1.5 [33X[0;0YTool functions[133X[101X
  
  [1X1.5-1 CanCompute[101X
  
  [29X[2XCanCompute[102X( [3XC[103X, [3Xs[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe  argument  is a category [23XC[123X and a string [23Xs[123X, which should be the name of a
  primitive  operation,  e.g., PreCompose. If applying this method is possible
  in  [23XC[123X,  the  method  returns [10Xtrue[110X, [10Xfalse[110X otherwise. If the string is not the
  name of a primitive operation, an error is raised.[133X
  
  [1X1.5-2 CheckConstructivenessOfCategory[101X
  
  [29X[2XCheckConstructivenessOfCategory[102X( [3XC[103X, [3Xs[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Ya list[133X
  
  [33X[0;0YThe  arguments  are  a  category  [23XC[123X  and  a  string [23Xs[123X. If [23Xs[123X is a categorical
  property  (e.g.  [10X"IsAbelianCategory"[110X),  the output is a list of strings with
  basic  operations  which  are  missing in [23XC[123X to have the categorical property
  constructively. If [23Xs[123X is not a categorical property, an error is raised.[133X
  
  
  [1X1.6 [33X[0;0YWell-Definedness of Cells[133X[101X
  
  [1X1.6-1 IsWellDefined[101X
  
  [29X[2XIsWellDefined[102X( [3Xc[103X ) [32X property
  [6XReturns:[106X  [33X[0;10Ya boolean[133X
  
  [33X[0;0YThe argument is a cell [23Xc[123X. The output is [10Xtrue[110X if [23Xc[123X is well-defined, otherwise
  the output is [10Xfalse[110X.[133X
  
  
  [1X1.7 [33X[0;0YType check[133X[101X
  
  [1X1.7-1 DisableBasicOperationTypeCheck[101X
  
  [29X[2XDisableBasicOperationTypeCheck[102X( [3Xcategory[103X ) [32X function
  [29X[2XEnableBasicOperationTypeCheck[102X( [3Xarg[103X ) [32X function
  
  [33X[0;0YMost  basic  operations have a prefunction, which does a (sometimes partial)
  typecheck  at  the  beginning  of  the  operation. These functions enable or
  disable this check for a category. (Enabled by default)[133X
  
