def test_categories():
from sympy.categories import (Object, Morphism, IdentityMorphism,
NamedMorphism, CompositeMorphism, Category,
Diagram, DiagramGrid)
A1 = Object("A1")
A2 = Object("A2")
A3 = Object("A3")
f1 = NamedMorphism(A1, A2, "f1")
f2 = NamedMorphism(A2, A3, "f2")
id_A1 = IdentityMorphism(A1)
K1 = Category("K1")
assert latex(A1) == "A_{1}"
assert latex(f1) == "f_{1}:A_{1}\\rightarrow A_{2}"
assert latex(id_A1) == "id:A_{1}\\rightarrow A_{1}"
assert latex(f2 * f1) == "f_{2}\\circ f_{1}:A_{1}\\rightarrow A_{3}"
assert latex(K1) == "\mathbf{K_{1}}"
d = Diagram()
assert latex(d) == "\emptyset"
d = Diagram({f1: "unique", f2: S.EmptySet})
assert latex(d) == "\\begin{Bmatrix}f_{2}\\circ f_{1}:A_{1}" \
"\\rightarrow A_{3} : \\emptyset, & id:A_{1}\\rightarrow " \
"A_{1} : \\emptyset, & id:A_{2}\\rightarrow A_{2} : " \
"\\emptyset, & id:A_{3}\\rightarrow A_{3} : \\emptyset, " \
"& f_{1}:A_{1}\\rightarrow A_{2} : \\left\\{unique\\right\\}, " \
"& f_{2}:A_{2}\\rightarrow A_{3} : \\emptyset\\end{Bmatrix}"
d = Diagram({f1: "unique", f2: S.EmptySet}, {f2 * f1: "unique"})
assert latex(d) == "\\begin{Bmatrix}f_{2}\\circ f_{1}:A_{1}" \
"\\rightarrow A_{3} : \\emptyset, & id:A_{1}\\rightarrow " \
"A_{1} : \\emptyset, & id:A_{2}\\rightarrow A_{2} : " \
"\\emptyset, & id:A_{3}\\rightarrow A_{3} : \\emptyset, " \
"& f_{1}:A_{1}\\rightarrow A_{2} : \\left\\{unique\\right\\}," \
" & f_{2}:A_{2}\\rightarrow A_{3} : \\emptyset\\end{Bmatrix}" \
"\\Longrightarrow \\begin{Bmatrix}f_{2}\\circ f_{1}:A_{1}" \
"\\rightarrow A_{3} : \\left\\{unique\\right\\}\\end{Bmatrix}"
# A linear diagram.
A = Object("A")
B = Object("B")
C = Object("C")
f = NamedMorphism(A, B, "f")
g = NamedMorphism(B, C, "g")
d = Diagram([f, g])
grid = DiagramGrid(d)
assert latex(grid) == "\\begin{array}{cc}\n" \
"A & B \\\\\n"\
" & C \n" \
"\\end{array}\n"
def test_category():
A = Object("A")
B = Object("B")
C = Object("C")
f = NamedMorphism(A, B, "f")
g = NamedMorphism(B, C, "g")
d1 = Diagram([f, g])
d2 = Diagram([f])
objects = d1.objects | d2.objects
K = Category("K", objects, commutative_diagrams=[d1, d2])
assert K.name == "K"
assert K.objects == Class(objects)
assert K.commutative_diagrams == FiniteSet(d1, d2)
raises(ValueError, lambda: Category(""))
def test_categories():
from sympy.categories import Object, NamedMorphism, IdentityMorphism, Category
A = Object("A")
B = Object("B")
f = NamedMorphism(A, B, "f")
id_A = IdentityMorphism(A)
K = Category("K")
assert str(A) == 'Object("A")'
assert str(f) == 'NamedMorphism(Object("A"), Object("B"), "f")'
assert str(id_A) == 'IdentityMorphism(Object("A"))'
assert str(K) == 'Category("K")'