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 Topics FrontPage Aldor FriCAS language SandBox SandBox Aldor Category Theory SandBox Aldor Category Theory 3 <-- You are here. aldor#include "axiom" #pile #library lBasics "basics.ao" #library lCategories "categories.ao" import from lBasics,lCategories +++ +++ Slice Category +++ Slice(Obj:Category,X:Obj):Category == with slice: % -> X SliceCategory(Obj:Category,X:Obj):Join(MathCategory Slice(Obj,X), Final Slice(Obj,X)) == add One():Slice(Obj,X) == W1:Slice(Obj,X) == add Rep == X; import from Rep slice:%->X == (x:%):X +-> rep x W1 add one(A:Slice(Obj,X)):(A->One()) == (a:A):One() +-> (slice a) pretend One() +++ +++ CoSlice Category +++ CoSlice(Obj:Category,X:Obj):Category == with coslice: X -> % CoSliceCategory(Obj:Category,X:Obj):Join(MathCategory CoSlice(Obj,X), Initial CoSlice(Obj,X)) == add Zero():CoSlice(Obj,X) == W2:CoSlice(Obj,X) == add Rep == X coslice:X->% == (x:X):% +-> per x W2 add zero(A:CoSlice(Obj,X)):(Zero()->A) == (z:Zero()):A +-> coslice (z pretend X) +++ +++ The Category of Pairs with pairs of morphisms as morphisms +++ Pair(Obj:Category):Category == with product: % -> (Obj,Obj) product: (Obj,Obj) ->% PairCategory(Obj:Category):MathCategory Pair Obj == add aldor Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/slicecategories.as using Aldor compiler and options -O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I$FRICAS/algebra Use the system command )set compiler args to change these options. The )library system command was not called after compilation. ... --Bill Page, Tue, 20 Nov 2007 20:26:04 -0800 replySandBox Aldor Category Theory 4

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