#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

   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 
      options.
#1 (Fatal Error) The file `axlit.ao' is newer than `categories.ao'.
   The )library system command was not called after compilation.