how to use SetMorphism?

[3f8450e1-87bf-41c6-ab53-29a0552debb3]

Hello every one,

I want create set bijections in sage...

sage: U = Set({'a', 'b', 'c', 'd'})
sage: V = Set({1,2,3,4})
sage: from sage.categories.morphism import SetMorphism
sage: bij = SetMorphism(
....:   Hom(U, V, Sets()),
....:   lambda l: {'a':1, 'b':2, 'c':3, 'd':4}[l]
....: )
sage: bij('a')
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-4-c2a304e84b3a> in <module>()
----> 1 bij('a')

/Users/elix/sage/newinst/cha/local/lib/python2.7/site-packages/sage/categories/map.so in sage.categories.map.Map.__call__ (sage/categories/map.c:5346)()

TypeError: a fails to convert into the map's domain {'a', 'c', 'b', 'd'}, but a `pushforward` method is not properly implemented

How to do this.?

CC: @nthiery

Component: categories

Keywords: morphism

Author: Jean-Baptiste Priez

Issue created by migration from https://trac.sagemath.org/ticket/17000

[nthiery]

comment:1

This is a known limitation which has been annoying for a while: at the end of Map.call, it's systematically checked that the parent of the result is the codomain of the map. In particular, the result should be an Element.

In other words, Map does not play well with facade parents, especially if the elements are plain Python objects.

I think there is a ticket about this, but I don't remember which from the top of my head.

Nice ticket number by the way :-)