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SandBox Aldor Category Theory 3

Edit detail for SandBox Aldor Category Theory 3 revision 6 of 7

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Editor: Bill Page Time: 2007/11/21 03:00:53 GMT-8
Note:

added:

aldor#include "axiom"
#pile
#library    lBasics  "basics.ao"
import from lBasics
#library    lCategories  "categories.ao"
import from 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/zope2/var/LatexWiki/slicecategories.as using AXIOM-XL 
      compiler and options 
-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
#1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
"/var/zope2/var/LatexWiki/slicecategories.as", line 15: 
SliceCategory(Obj:Category,X:Obj):Join(MathCategory Slice(Obj,X), Final Slice(Obj,X)) == add
.........................................................................................^
[L15 C90] #2 (Error) The domain is missing some exports.
        Missing Aut: (A: Slice(Slice(Slice(Slice(Obj, X), X), X), X)) -> Automorphi...
        Missing End: (A: Slice(Slice(Slice(Slice(Obj, X), X), X), X)) -> Endomorphi...
        Missing One: () -> Slice(Obj, X)
        Missing one: (A: Slice(Obj, X)) -> A -> One()
"/var/zope2/var/LatexWiki/slicecategories.as", line 29: 
CoSliceCategory(Obj:Category,X:Obj):Join(MathCategory CoSlice(Obj,X), Initial CoSlice(Obj,X)) == add
.................................................................................................^
[L29 C98] #3 (Error) The domain is missing some exports.
        Missing Aut: (A: CoSlice(CoSlice(CoSlice(CoSlice(Obj, X), X), X), X)) -> Au...
        Missing End: (A: CoSlice(CoSlice(CoSlice(CoSlice(Obj, X), X), X), X)) -> En...
        Missing Zero: () -> CoSlice(Obj, X)
        Missing zero: (A: CoSlice(Obj, X)) -> Zero() -> A
"/var/zope2/var/LatexWiki/slicecategories.as", line 44: 
PairCategory(Obj:Category):MathCategory Pair Obj == add
....................................................^
[L44 C53] #4 (Error) The domain is missing some exports.
        Missing Aut: (A: Pair(Pair(Pair(Pair(Obj))))) -> AutomorphismCategory(Pair(...
        Missing End: (A: Pair(Pair(Pair(Pair(Obj))))) -> EndomorphismCategory(Pair(...
   The )library system command was not called after compilation.

... --Bill Page, Tue, 20 Nov 2007 20:26:04 -0800 reply

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