diff --git a/README.md b/README.md
index 0e8e946..22163ae 100644
--- a/README.md
+++ b/README.md
@@ -127,6 +127,47 @@ let schema: JSONSchema = .object(
 )
 ```
 
+### Schema Properties
+
+Access schema metadata and type information through convenience properties:
+
+```swift
+import JSONSchema
+
+let schema: JSONSchema = .object(
+    title: "Person",
+    description: "A human being",
+    properties: [
+        "name": .string,
+        "age": .integer
+    ]
+)
+
+// Access metadata
+print(schema.typeName) // "object"
+print(schema.title) // "Person"
+print(schema.description) // "A human being"
+```
+
+### JSON Value Compatibility
+
+The library provides methods to check compatibility between JSON values and schemas:
+
+```swift
+import JSONSchema
+
+// Check if a JSON value is compatible with a schema
+let value: JSONValue = 42
+let schema: JSONSchema = .integer(minimum: 0)
+let isCompatible = value.isCompatible(with: schema) // true
+
+// Strict vs non-strict compatibility
+let numberValue: JSONValue = 42
+let numberSchema: JSONSchema = .number()
+let strictCompatible = numberValue.isCompatible(with: numberSchema) // false
+let nonStrictCompatible = numberValue.isCompatible(with: numberSchema, strict: false) // true
+```
+
 ### Schema Serialization
 
 ```swift
@@ -135,7 +176,7 @@ import JSONSchema
 // Create a schema
 let schema: JSONSchema = .object(
     title: "Person",
-    description: "A person schema",
+    description: "A human being",
     properties: [
         "name": .string(),
         "age": .integer(minimum: 0)
diff --git a/Sources/JSONSchema/JSONSchema.swift b/Sources/JSONSchema/JSONSchema.swift
index b0183c4..74a735d 100644
--- a/Sources/JSONSchema/JSONSchema.swift
+++ b/Sources/JSONSchema/JSONSchema.swift
@@ -353,22 +353,22 @@ extension JSONSchema {
     /// The name of the schema type.
     public var typeName: String {
         switch self {
-        case .object: return "Object"
-        case .array: return "Array"
-        case .string: return "String"
-        case .number: return "Number"
-        case .integer: return "Integer"
-        case .boolean: return "Boolean"
-        case .null: return "Null"
-        case .reference: return "Reference"
-        case .anyOf: return "AnyOf"
-        case .allOf: return "AllOf"
-        case .oneOf: return "OneOf"
-        case .not: return "Not"
-        case .empty: return "Empty"
-        case .any: return "Any"
+        case .object: return "object"
+        case .array: return "array"
+        case .string: return "string"
+        case .number: return "number"
+        case .integer: return "integer"
+        case .boolean: return "boolean"
+        case .null: return "null"
+        case .reference: return "reference"
+        case .anyOf: return "anyOf"
+        case .allOf: return "allOf"
+        case .oneOf: return "oneOf"
+        case .not: return "not"
+        case .empty: return "empty"
+        case .any: return "any"
         @unknown default:
-            return "Unknown"
+            return "unknown"
         }
     }
 
diff --git a/Tests/JSONSchemaTests/JSONSchemaTests.swift b/Tests/JSONSchemaTests/JSONSchemaTests.swift
index 4604582..0df57ab 100644
--- a/Tests/JSONSchemaTests/JSONSchemaTests.swift
+++ b/Tests/JSONSchemaTests/JSONSchemaTests.swift
@@ -1028,59 +1028,59 @@ import Testing
 @Test func testTypeName() {
     // Test object schema
     let objectSchema: JSONSchema = .object()
-    #expect(objectSchema.typeName == "Object")
+    #expect(objectSchema.typeName == "object")
 
     // Test array schema
     let arraySchema: JSONSchema = .array()
-    #expect(arraySchema.typeName == "Array")
+    #expect(arraySchema.typeName == "array")
 
     // Test string schema
     let stringSchema: JSONSchema = .string()
-    #expect(stringSchema.typeName == "String")
+    #expect(stringSchema.typeName == "string")
 
     // Test number schema
     let numberSchema: JSONSchema = .number()
-    #expect(numberSchema.typeName == "Number")
+    #expect(numberSchema.typeName == "number")
 
     // Test integer schema
     let integerSchema: JSONSchema = .integer()
-    #expect(integerSchema.typeName == "Integer")
+    #expect(integerSchema.typeName == "integer")
 
     // Test boolean schema
     let booleanSchema: JSONSchema = .boolean()
-    #expect(booleanSchema.typeName == "Boolean")
+    #expect(booleanSchema.typeName == "boolean")
 
     // Test null schema
     let nullSchema: JSONSchema = .null
-    #expect(nullSchema.typeName == "Null")
+    #expect(nullSchema.typeName == "null")
 
     // Test reference schema
     let referenceSchema: JSONSchema = .reference("#/definitions/Person")
-    #expect(referenceSchema.typeName == "Reference")
+    #expect(referenceSchema.typeName == "reference")
 
     // Test anyOf schema
     let anyOfSchema: JSONSchema = .anyOf([.string(), .integer()])
-    #expect(anyOfSchema.typeName == "AnyOf")
+    #expect(anyOfSchema.typeName == "anyOf")
 
     // Test allOf schema
     let allOfSchema: JSONSchema = .allOf([.string(), .integer()])
-    #expect(allOfSchema.typeName == "AllOf")
+    #expect(allOfSchema.typeName == "allOf")
 
     // Test oneOf schema
     let oneOfSchema: JSONSchema = .oneOf([.string(), .integer()])
-    #expect(oneOfSchema.typeName == "OneOf")
+    #expect(oneOfSchema.typeName == "oneOf")
 
     // Test not schema
     let notSchema: JSONSchema = .not(.string())
-    #expect(notSchema.typeName == "Not")
+    #expect(notSchema.typeName == "not")
 
     // Test empty schema
     let emptySchema: JSONSchema = .empty
-    #expect(emptySchema.typeName == "Empty")
+    #expect(emptySchema.typeName == "empty")
 
     // Test any schema
     let anySchema: JSONSchema = .any
-    #expect(anySchema.typeName == "Any")
+    #expect(anySchema.typeName == "any")
 }
 
 @Test func testTypeDefault() {