gh-36572: Replace relative imports by absolute ones in categories

    
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As preparation for compiling with meson, we replace relative imports by
absolute ones.
Relative imports are not used consistently in the codebase and result in
issues for doctesting with pytest (which admittedly is a limitation of
pytest). We normalize the relative imports in `sage.categories` to be
absolute imports. Small code-style improvements along the way (mainly to
nicely order the imports)

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URL: #36572
Reported by: Tobias Diez
Reviewer(s): Dima Pasechnik

src/sage/categories/action.pxd

@@ -1,7 +1,7 @@
 from sage.structure.element cimport Element
-from .morphism cimport Morphism
-from .map cimport Map
-from .functor cimport Functor
+from sage.categories.morphism cimport Morphism
+from sage.categories.map cimport Map
+from sage.categories.functor cimport Functor
 
 cdef class Action(Functor):
     cdef readonly G

src/sage/categories/action.pyx

@@ -56,13 +56,13 @@ AUTHOR:
 
 from cpython.tuple cimport PyTuple_GET_ITEM
 
-from .functor cimport Functor
-from .morphism cimport Morphism
-from .map cimport Map
+from sage.categories.functor cimport Functor
+from sage.categories.morphism cimport Morphism
+from sage.categories.map cimport Map
 from sage.structure.element cimport parent
 from sage.structure.parent cimport Parent
 
-from . import homset
+from sage.categories import homset
 from weakref import ref
 
 

src/sage/categories/algebra_ideals.py

@@ -10,10 +10,10 @@
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
 
-from .algebra_modules import AlgebraModules
-from .algebras import Algebras
-from .rings import Rings
-from .category_types import Category_ideal
+from sage.categories.algebra_modules import AlgebraModules
+from sage.categories.algebras import Algebras
+from sage.categories.category_types import Category_ideal
+from sage.categories.rings import Rings
 
 
 class AlgebraIdeals(Category_ideal):

src/sage/categories/algebra_modules.py

@@ -10,10 +10,11 @@
 #                  http://www.gnu.org/licenses/
 #******************************************************************************
 
-from .category_types import Category_module
-from .commutative_algebras import CommutativeAlgebras
-from .commutative_rings import CommutativeRings
-from .modules import Modules
+from sage.categories.category_types import Category_module
+from sage.categories.commutative_algebras import CommutativeAlgebras
+from sage.categories.commutative_rings import CommutativeRings
+from sage.categories.modules import Modules
+
 
 class AlgebraModules(Category_module):
     """

src/sage/categories/algebras_with_basis.py

@@ -9,13 +9,13 @@
 #                  https://www.gnu.org/licenses/
 #******************************************************************************
 
+from sage.categories.cartesian_product import CartesianProductsCategory
+from sage.categories.category_with_axiom import CategoryWithAxiom_over_base_ring
+from sage.categories.tensor import TensorProductsCategory, tensor
+from sage.categories.unital_algebras import UnitalAlgebras
 from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.lazy_import import LazyImport
-from sage.categories.tensor import TensorProductsCategory, tensor
-from sage.categories.cartesian_product import CartesianProductsCategory
-from sage.categories.category_with_axiom import CategoryWithAxiom_over_base_ring
-from .unital_algebras import UnitalAlgebras
 
 
 class AlgebrasWithBasis(CategoryWithAxiom_over_base_ring):

src/sage/categories/all.py

@@ -27,128 +27,128 @@
 from sage.misc.namespace_package import install_doc
 install_doc(__package__, __doc__)
 
-from . import primer
+from sage.categories import primer
 
 from sage.misc.lazy_import import lazy_import
 
-from .all__sagemath_objects import *
+from sage.categories.all__sagemath_objects import *
 
-from .basic import *
+from sage.categories.basic import *
 
-from .chain_complexes import ChainComplexes, HomologyFunctor
+from sage.categories.chain_complexes import ChainComplexes, HomologyFunctor
 
-from .simplicial_complexes import SimplicialComplexes
+from sage.categories.simplicial_complexes import SimplicialComplexes
 
-from .tensor import tensor
-from .signed_tensor import tensor_signed
+from sage.categories.tensor import tensor
+from sage.categories.signed_tensor import tensor_signed
 
-from .g_sets import GSets
-from .pointed_sets import PointedSets
+from sage.categories.g_sets import GSets
+from sage.categories.pointed_sets import PointedSets
 
-from .sets_with_grading import SetsWithGrading
+from sage.categories.sets_with_grading import SetsWithGrading
 
-from .groupoid import Groupoid
-from .permutation_groups import PermutationGroups
+from sage.categories.groupoid import Groupoid
+from sage.categories.permutation_groups import PermutationGroups
 
 # enumerated sets
-from .finite_sets import FiniteSets
-from .enumerated_sets import EnumeratedSets
-from .finite_enumerated_sets import FiniteEnumeratedSets
-from .infinite_enumerated_sets import InfiniteEnumeratedSets
+from sage.categories.finite_sets import FiniteSets
+from sage.categories.enumerated_sets import EnumeratedSets
+from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
+from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 
 # posets
-from .posets import Posets
-from .finite_posets import FinitePosets
-from .lattice_posets import LatticePosets
-from .finite_lattice_posets import FiniteLatticePosets
+from sage.categories.posets import Posets
+from sage.categories.finite_posets import FinitePosets
+from sage.categories.lattice_posets import LatticePosets
+from sage.categories.finite_lattice_posets import FiniteLatticePosets
 
 # finite groups/...
-from .finite_semigroups import FiniteSemigroups
-from .finite_monoids import FiniteMonoids
-from .finite_groups import FiniteGroups
-from .finite_permutation_groups import FinitePermutationGroups
+from sage.categories.finite_semigroups import FiniteSemigroups
+from sage.categories.finite_monoids import FiniteMonoids
+from sage.categories.finite_groups import FiniteGroups
+from sage.categories.finite_permutation_groups import FinitePermutationGroups
 
 # fields
-from .number_fields import NumberFields
-from .function_fields import FunctionFields
+from sage.categories.number_fields import NumberFields
+from sage.categories.function_fields import FunctionFields
 
 # modules
-from .left_modules import LeftModules
-from .right_modules import RightModules
-from .bimodules import Bimodules
+from sage.categories.left_modules import LeftModules
+from sage.categories.right_modules import RightModules
+from sage.categories.bimodules import Bimodules
 
-from .modules import Modules
+from sage.categories.modules import Modules
 RingModules = Modules
-from .vector_spaces import VectorSpaces
+from sage.categories.vector_spaces import VectorSpaces
 
 # (hopf) algebra structures
-from .algebras import Algebras
-from .commutative_algebras import CommutativeAlgebras
-from .coalgebras import Coalgebras
-from .bialgebras import Bialgebras
-from .hopf_algebras import HopfAlgebras
-from .lie_algebras import LieAlgebras
+from sage.categories.algebras import Algebras
+from sage.categories.commutative_algebras import CommutativeAlgebras
+from sage.categories.coalgebras import Coalgebras
+from sage.categories.bialgebras import Bialgebras
+from sage.categories.hopf_algebras import HopfAlgebras
+from sage.categories.lie_algebras import LieAlgebras
 
 # specific algebras
-from .monoid_algebras import MonoidAlgebras
-from .group_algebras import GroupAlgebras
-from .matrix_algebras import MatrixAlgebras
+from sage.categories.monoid_algebras import MonoidAlgebras
+from sage.categories.group_algebras import GroupAlgebras
+from sage.categories.matrix_algebras import MatrixAlgebras
 
 # ideals
-from .ring_ideals import RingIdeals
+from sage.categories.ring_ideals import RingIdeals
 Ideals = RingIdeals
-from .commutative_ring_ideals import CommutativeRingIdeals
-from .algebra_modules import AlgebraModules
-from .algebra_ideals import AlgebraIdeals
-from .commutative_algebra_ideals import CommutativeAlgebraIdeals
+from sage.categories.commutative_ring_ideals import CommutativeRingIdeals
+from sage.categories.algebra_modules import AlgebraModules
+from sage.categories.algebra_ideals import AlgebraIdeals
+from sage.categories.commutative_algebra_ideals import CommutativeAlgebraIdeals
 
 # schemes and varieties
-from .modular_abelian_varieties import ModularAbelianVarieties
-from .schemes import Schemes
+from sage.categories.modular_abelian_varieties import ModularAbelianVarieties
+from sage.categories.schemes import Schemes
 
 # * with basis
-from .modules_with_basis import ModulesWithBasis
+from sage.categories.modules_with_basis import ModulesWithBasis
 FreeModules = ModulesWithBasis
-from .hecke_modules            import HeckeModules
-from .algebras_with_basis      import AlgebrasWithBasis
-from .coalgebras_with_basis    import CoalgebrasWithBasis
-from .bialgebras_with_basis    import BialgebrasWithBasis
-from .hopf_algebras_with_basis import HopfAlgebrasWithBasis
+from sage.categories.hecke_modules            import HeckeModules
+from sage.categories.algebras_with_basis      import AlgebrasWithBasis
+from sage.categories.coalgebras_with_basis    import CoalgebrasWithBasis
+from sage.categories.bialgebras_with_basis    import BialgebrasWithBasis
+from sage.categories.hopf_algebras_with_basis import HopfAlgebrasWithBasis
 
 # finite dimensional * with basis
-from .finite_dimensional_modules_with_basis       import FiniteDimensionalModulesWithBasis
-from .finite_dimensional_algebras_with_basis      import FiniteDimensionalAlgebrasWithBasis
-from .finite_dimensional_coalgebras_with_basis    import FiniteDimensionalCoalgebrasWithBasis
-from .finite_dimensional_bialgebras_with_basis    import FiniteDimensionalBialgebrasWithBasis
-from .finite_dimensional_hopf_algebras_with_basis import FiniteDimensionalHopfAlgebrasWithBasis
+from sage.categories.finite_dimensional_modules_with_basis       import FiniteDimensionalModulesWithBasis
+from sage.categories.finite_dimensional_algebras_with_basis      import FiniteDimensionalAlgebrasWithBasis
+from sage.categories.finite_dimensional_coalgebras_with_basis    import FiniteDimensionalCoalgebrasWithBasis
+from sage.categories.finite_dimensional_bialgebras_with_basis    import FiniteDimensionalBialgebrasWithBasis
+from sage.categories.finite_dimensional_hopf_algebras_with_basis import FiniteDimensionalHopfAlgebrasWithBasis
 
 # graded *
-from .graded_modules       import GradedModules
-from .graded_algebras      import GradedAlgebras
-from .graded_coalgebras    import GradedCoalgebras
-from .graded_bialgebras    import GradedBialgebras
-from .graded_hopf_algebras import GradedHopfAlgebras
+from sage.categories.graded_modules       import GradedModules
+from sage.categories.graded_algebras      import GradedAlgebras
+from sage.categories.graded_coalgebras    import GradedCoalgebras
+from sage.categories.graded_bialgebras    import GradedBialgebras
+from sage.categories.graded_hopf_algebras import GradedHopfAlgebras
 
 # graded * with basis
-from .graded_modules_with_basis       import GradedModulesWithBasis
-from .graded_algebras_with_basis      import GradedAlgebrasWithBasis
-from .graded_coalgebras_with_basis    import GradedCoalgebrasWithBasis
-from .graded_bialgebras_with_basis    import GradedBialgebrasWithBasis
-from .graded_hopf_algebras_with_basis import GradedHopfAlgebrasWithBasis
+from sage.categories.graded_modules_with_basis       import GradedModulesWithBasis
+from sage.categories.graded_algebras_with_basis      import GradedAlgebrasWithBasis
+from sage.categories.graded_coalgebras_with_basis    import GradedCoalgebrasWithBasis
+from sage.categories.graded_bialgebras_with_basis    import GradedBialgebrasWithBasis
+from sage.categories.graded_hopf_algebras_with_basis import GradedHopfAlgebrasWithBasis
 
 # Coxeter groups
-from .coxeter_groups import CoxeterGroups
+from sage.categories.coxeter_groups import CoxeterGroups
 lazy_import('sage.categories.finite_coxeter_groups', 'FiniteCoxeterGroups')
-from .weyl_groups import WeylGroups
-from .finite_weyl_groups import FiniteWeylGroups
-from .affine_weyl_groups import AffineWeylGroups
+from sage.categories.weyl_groups import WeylGroups
+from sage.categories.finite_weyl_groups import FiniteWeylGroups
+from sage.categories.affine_weyl_groups import AffineWeylGroups
 
 # crystal bases
-from .crystals import Crystals
-from .highest_weight_crystals import HighestWeightCrystals
-from .regular_crystals import RegularCrystals
-from .finite_crystals import FiniteCrystals
-from .classical_crystals import ClassicalCrystals
+from sage.categories.crystals import Crystals
+from sage.categories.highest_weight_crystals import HighestWeightCrystals
+from sage.categories.regular_crystals import RegularCrystals
+from sage.categories.finite_crystals import FiniteCrystals
+from sage.categories.classical_crystals import ClassicalCrystals
 
 # polyhedra
 lazy_import('sage.categories.polyhedra', 'PolyhedralSets')

src/sage/categories/all__sagemath_objects.py

@@ -4,28 +4,25 @@
 
 # Resolve a circular import so that "import sage.categories.all" can succeed
 # in initializing the category system.
-import sage.structure.category_object    # imports sage.categories.category
+import sage.structure.category_object  # imports sage.categories.category
 
-# Small part of "from .basic import *":
-from .objects import Objects
-from .sets_cat import Sets, EmptySetError
+# Small part of "from sage.categories.basic import *":
+from sage.categories.objects import Objects
+from sage.categories.sets_cat import Sets, EmptySetError
 
 
-from .category import Category
+from sage.categories.category import Category
 
-from .category_types import Elements
+from sage.categories.category_types import Elements
 
-from .cartesian_product import cartesian_product
+from sage.categories.cartesian_product import cartesian_product
 
-from .functor  import (ForgetfulFunctor,
-                      IdentityFunctor)
+from sage.categories.functor import ForgetfulFunctor, IdentityFunctor
 
-from .homset   import (Hom, hom,
-                      End, end,
-                      Homset, HomsetWithBase)
+from sage.categories.homset import Hom, hom, End, end, Homset, HomsetWithBase
 
-from .morphism import Morphism
+from sage.categories.morphism import Morphism
 
-from .realizations import Realizations
+from sage.categories.realizations import Realizations
 
-from .sets_with_partial_maps import SetsWithPartialMaps
+from sage.categories.sets_with_partial_maps import SetsWithPartialMaps