\ Tpf      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcde    ,  Rule type #Declares equality of two morphisms Morphism data type $Naturally transformational modifier Functionional modifier Composition of morphisms Tensor product of morphisms Identity morphism Atomary morphism "Types of the functional modifier. Contravariant functor Covariant functor Function on objects fghijClass of morphisms. &Returns domain of the given morphism. (Returns codomain of the given morphism. Checks whether morphism is id. 6Composition of two morphisms (should be associative). !Tensor product of two morphisms. 6Normalizes the term representing morphism, e.g. turns ((a * b) * c) to (a * b * c) /Checks whether morphism is an atomary formula. Creates ; by morphism information (e.g. name), domain and codomain. VCreates generalized element, i.e. an arrow from the tensorial Id to the given object. \Creates generalized coelement, i.e. an arrow from the the given object to the tensorial Id. !Creates object (actually it's id). Same as ". "Creates object id. Same as !. #Tensorial Id, tid * f == f in strict monoidal category. kl$Turns recursively (a \* b) \. (c \* d) to (a \. c) \* (b \. d). %Turns recursively (a \. c) \* (b \. d) to (a \* b) \. (c \* d). mnopq&ACollects atomary subterms of the given arrow as keys of the map. 'x \== y is the same as   x y ( Applies the   to the given morphism  !"#$%&'(    !"#$%& '(    !"#$%&'()Labelled arrow data type. *+,-./0)Removes labels and returns corresponding  . 10Returns the label of the given marked morphism. 2?Applies operation to the marked subterm of the given morphism. 3?Applies operation to the marked subterm of the given morphism. 4 0 $ 3 s lf op5MChooses subterm of an associative operation (composition or tensor product). 6&Returns the given morphism marked up. )*+,-./0123456)/.-,+*6043251)/.-,+**+,-./0123456789"789rstuvwxyz{|}~78978989,:For given object create it' s left dual:  (http://en.wikipedia.org/wiki/Dual_object. ;Same as :, for usage in calculations. <Same as :", for usage in rule descriptions. =For given object create it's right dual:  (http://en.wikipedia.org/wiki/Dual_object. >Same as =, for usage in calculations. ?Same as =", for usage in rule descriptions. @For given dual pair of objects (x, y) and name nm call unit' of nm x y to create named ( duality unit arrow. Generates error if (x, y) is not a dual pair. ASame as @ "\\eta", for usage in calculations. BSame as @ "*\\eta"6, except that it does not check duality. For usage in  rule descriptions. CFor given dual pair of objects (x, y) and name nm call counit' of nm x y to create named * duality counit arrow. Generates error if (x, y) is not a dual pair. DSame as C "\\epsilon", for usage in calculations. ESame as C "*\\epsilon"6, except that it does not check duality. For usage in  rule descriptions. FOne of " zigzag rules" for duality. GOne of " zigzag rules" for duality. HFor given pair of objects (x, y) and name nm call braid' of nm x y to create named  braid arrow:  6http://en.wikipedia.org/wiki/Braided_monoidal_category ISame as H "\\beta", for usage in calculations. JSame as H "*\\beta"", for usage in rule descriptions. KFor given pair of objects (x, y) and name nm call unbraid' of nm x y to create named ) unbraid arrow (inverse of braid arrow). LSame as K "\\ beta^{-1}", for usage in calculations. MSame as K "*\\ beta^{-1}"", for usage in rule descriptions. NIsomorphism rule: L as inverse of I. OIsomorphism rule: I as inverse of L. PNaturality rule on the " left wire". QNaturality rule on the " right wire". RHexagon identity for I, strict monoidal case. SHexagon identity for L, strict monoidal case. T Rule for the "cross" arrow: it's simply self-inverse braid. UFor given object x and name nm call twist'of nm x to create named  twist arrow. VSame as U "\\theta", for usage in calculations. WSame as U "*\\theta"", for usage in rule descriptions. XFor given object x and name nm call untwist'of nm x to create named  untwist arrow. YSame as X "\\ theta^{-1}", for usage in calculations. ZSame as X "*\\ theta^{-1}"", for usage in rule descriptions. [Isomorphism rule: Y as inverse of V. \Isomorphism rule: V as inverse of Y. ]'Twisting tensorial Id changes nothing. ^Twisting naturality. _Twist/braid interaction. `dagger'of f' creates daggered version of the arrow f. aSame as `, for usage in calculations. bSame as `", for usage in rule descriptions. cAs contravariant functor a maps id's to id's. da swaps domain and codomain. ea involution rule. 0:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcde,:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcde,:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcde      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijkklmnopqrstuvwxyz{|}~ Monocle-0.0.3 Monocle.Utils Monocle.CoreMonocle.Markup Monocle.Tex Monocle.RulesWrap PrintablestrMStackpoppushtappendtcombineRuleDefEqualMor TransformFunc CompositionTensorIdArrowFuncT CofunctorFunctorFunctionMorphismdomcodisId\.\*nrmatomaryarrowelement coelementobjectobjectIdtidverthorzcollect\==applyLab MTransformMFunc MCompositionMTensorMIdMArrowunmarkgetLabelmodifLabmodif'modifchoosemarkupTexifiedtexdocldual'ofldualldual'rrdual'ofrdualrdual'runit'ofunitunit'r counit'ofcounitcounit'rzigzag'rule'Leftzigzag'rule'Rightbraid'ofbraidbraid'r unbraid'ofunbraid unbraid'rbraid'rule'Iso'Leftbraid'rule'Iso'Rightbraid'rule'Nat'Leftbraid'rule'Nat'Rightbraid'rule'Hex'Braidbraid'rule'Hex'Unbraid cross'ruletwist'oftwisttwist'r untwist'ofuntwist untwist'runtwist'rule'Iso'Leftuntwist'rule'Iso'Right twist'rule'Idtwist'rule'Naturaltwist'rule'Braid dagger'ofdaggerdagger'rdagger'rule'Iddagger'rule'Cofunctordagger'rule'Inv ArrowDatadom'cod'isId'widthheightmapMorMmapMorM'mergesubstsubst's'joint'subt'supt'idt'opt'ropt'opent'closet'cmdt'sft'begint'endt'endlt'matht'docMap t'docType_ t'docHead_ t'itemizet'doc_t'texF_t'texNaturalTfm_t'texMort'objMortexObjt'mblabt'texLabt'objLab texObjLabptexpobjpdocobAobBobCobD