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#include "axiom"
#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
   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/slicecategories.as using AXIOM-XL 
      compiler and options 
-O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I $AXIOM/algebra
      Use the system command )set compiler args to change these 
#1 (Fatal Error) The file `BOOLEAN.ao' is newer than `basics.ao'.
   The )library system command was not called after compilation.

SandBox Aldor Category Theory 4

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