update database documentation based on new schema

Author: ScriptRaccoon

DATABASE.md

@@ -4,74 +4,114 @@
 
 _CatDat_ is based on a [SQLite database](https://sqlite.org/). During runtime of the application, it is read-only.
 
-The local copy of the database is located at `/databases/catdat/catdat.db`. It has three main tables:
+The local copy of the database is located at `/databases/catdat/catdat.db`. It contains three main tables:
+
+- `structures`
+- `properties`
+- `implications`
+
+The `structures` table stores data that is common to all types of categorical structures. Two types are currently supported: categories and functors. They are stored in the following table:
+
+- `structure_types`
+
+Structure-specific data is stored in additional tables, such as:
 
 - `categories`
-- `category_properties`
-- `category_implications`
+- `functors`
 
-To associate properties with categories (satisfied or not), there is a table:
+Properties (whether satisfied or not) are associated with categorical structures via the following table:
 
-- `category_property_assignments`
+- `property_assignments`
 
 To mark properties as assumptions or conclusions of an implication, there are two tables:
 
-- `category_implication_assumptions`
-- `category_implication_conclusions`
+- `assumptions`
+- `conclusions`
 
-But they are abstracted away by using the view `category_implications_view`.
+These tables are abstracted through the `implications_view` view.
 
-Further tables are:
+Functor implications may also depend on properties of the source or target category. Such dependencies are stored in the following tables:
 
-- `category_tags`
-- `category_tag_assignments`
-- `related_categories`
-- `relations`
-- `special_object_types`
-- `special_objects`
-- `special_morphism_types`
-- `special_morphisms`
-- `related_category_properties`
-- `category_comments`
+- `source_assumptions`
+- `target_assumptions`
 
-For functors there are similar tables, such as:
-
-- `functors`
-- `functor_properties`
-- `functor_implications`
-- `functor_property_assignments`
+Additional tables are available. For a complete overview, see the diagram below.
 
 ## Schema vs. Data
 
-The schema defines the structure of the database: tables, views, indexes, and triggers. It is specified in several SQL files located in the subfolder [/databases/catdat/schema](/databases/catdat/schema/). The command `pnpm db:setup` deletes the old database file (if it exists) and creates a new one using this schema. This is required when the schema changes, so it is recommended to run it periodically.
+The schema defines the structure of the database: tables, views, indexes, and triggers. It is specified in several SQL files located in the subfolder [/databases/catdat/schema](/databases/catdat/schema/). The command
+
+```
+pnpm db:setup
+```
+
+deletes the old database file (if it exists) and creates a new one using this schema. This is required when the schema changes.
+
+Database entries (categories, functors, properties, implications, etc.) are defined in YAML files located in the subfolder [/databases/catdat/data](/databases/catdat/data/). The command
+
+```
+pnpm db:seed
+```
 
-Database entries (categories, properties, implications, etc.) are defined in YAML files located in the subfolder [/databases/catdat/data](/databases/catdat/data/). The command `pnpm db:seed` rebuilds the database by clearing all existing data and then parsing and inserting the entries defined in these YAML files.
+rebuilds the database by clearing all existing data and then parsing and inserting the entries defined in these YAML files.
 
 ## Derived Data
 
-From the defined satisfied properties of a given category, new properties can be automatically deduced using the implications. (For example, when a category has equalizers and products, we can infer that it is complete.) The same applies to unsatisfied properties. Additionally, suitable implications may be dualized, and a category inherits all dualized properties of its dual category, if available. Note that the YAML files mentioned above do _not_ contain any derived data.
+From the defined satisfied properties of a given categorical structure, new properties can be automatically deduced using the implications. (For example, when a category has equalizers and products, we can infer that it is complete.) The same applies to unsatisfied properties.
 
-The command `pnpm db:deduce` deduces implications, satisfied properties, and unsatisfied properties.
+Additionally, suitable implications may be dualized, and a categorical structure inherits all dualized properties of its dual structure, if available. Note that the YAML files mentioned above do _not_ contain any derived data.
+
+The command
+
+```
+pnpm db:deduce
+```
+
+deduces implications, satisfied properties, and unsatisfied properties.
 
 ## Test Data
 
-The command `pnpm db:test` executes some tests and verifies that the data behaves as expected.
+The command
+
+```
+pnpm db:test
+```
+
+executes some tests and verifies that the data behaves as expected.
 
 ## One command for everything
 
-Use `pnpm db:update` to run all the commands in sequence: `pnpm db:seed`,`pnpm db:deduce`, and `pnpm db:test`.
+Use the command
+
+```
+pnpm db:update
+```
 
-Use `pnpm db:watch` to run this command automatically every time a file in the subfolder [/databases/catdat/data](/databases/catdat/data) changes. This is useful in particular during development.
+to run all the commands in sequence: `pnpm db:seed`,`pnpm db:deduce`, and `pnpm db:test`. This also creates a copy of the local database in the `/static` folder.
+
+Use
+
+```
+pnpm db:watch
+```
+
+to run this command automatically every time a file in the subfolder [/databases/catdat/data](/databases/catdat/data) changes. This is useful in particular during development.
 
 ## Redundancies
 
-There is another script that intentionally does not run with each update: `pnpm db:redundancies` checks for redundant assignments of properties to categories.
+There is another script that intentionally does not run with each update. Use the command
+
+```
+pnpm db:redundancies
+```
+
+to check for redundant assignments of properties to categorical structures.
 
 ## Diagram
 
-This is the database schema as of 26.05.2026; changes may occur.
+This is the database schema as of 15.06.2026; changes may occur.
 
-<img alt="database diagram" src="https://github.com/user-attachments/assets/c8ce7e30-874b-4130-9ff5-2fc368f87f15" />
+<img alt="database diagram" src="https://github.com/user-attachments/assets/fc2cc524-3de3-4974-8929-9f73a2df62d7" />
 
 ## Application Database