AWS SAM template for serverless::api not creating cognito user pool authorizer

I can't figure out why after deploying this template I don't see any Authorizer for this API under the "Authorizers" tab on AWS console.

AWSTemplateFormatVersion: '2010-09-09'
Transform: AWS::Serverless-2016-10-31
Description: >
  Description here

Globals:
  Function:
    Timeout: 3

Resources:
 
  ProductGet:
    Type: AWS::Serverless::Function 
    Properties:
      CodeUri: ./
      Handler: product-get.lambda_handler
      Runtime: python3.8
      Role: "particular role here"
      Events:
        ProductGet:
          Type: Api 
          Properties:
            Path: /product-get
            Method: post
            Auth:
              Authorizers:
                MyCognitoAuth:
                 UserPoolArn: "user pool arn here"
                 AuthType: "COGNITO_USER_POOLS"
              DefaultAuthorizer: MyCognitoAuth

Figured out it. You cannot define authorizers in "Events" section. If your API needs an authorizer, you'll have to define that API as a separate resource and link it to the events using APIid.

Sample code below.

MyApi:
    Type: AWS::Serverless::Api
    Properties:
      StageName: Prod
      Auth:
        DefaultAuthorizer: MyCognitoAuth # OPTIONAL
        Authorizers:
          MyCognitoAuth:
            Type: COGNITO_USER_POOLS
            # Can also accept an array
            UserPoolArn: "user pool arn here"

  ProductGet:
    Type: AWS::Serverless::Function         
    Properties:
      CodeUri: ./
      Handler: product-get.lambda_handler
      Runtime: python3.8
      Role: 'role ARN here'
      Events:
        ProductGet:
          Type: Api 
          Properties:
            Path: /product-get
            Method: post
            RestApiId: !Ref MyApi #This is how you need to refer to your API
            Auth:
              Authorizer: MyCognitoAuth