feat(backend): add database models

backend/src/models/category.py

@@ -0,0 +1,25 @@
+from typing import TYPE_CHECKING
+
+from sqlalchemy import String, Text
+from sqlalchemy.orm import Mapped, mapped_column, relationship
+
+from src.models.base import Base, UUIDMixin
+
+if TYPE_CHECKING:
+    from src.models.question import Question
+
+
+class Category(Base, UUIDMixin):
+    """Question category (e.g., Arrays, Strings, Trees)."""
+
+    __tablename__ = "categories"
+
+    name: Mapped[str] = mapped_column(String(100), unique=True, nullable=False)
+    slug: Mapped[str] = mapped_column(String(100), unique=True, nullable=False)
+    description: Mapped[str | None] = mapped_column(Text, nullable=True)
+
+    # Relationships
+    questions: Mapped[list["Question"]] = relationship(
+        secondary="question_categories",
+        back_populates="categories",
+    )