If you’re been hoping to find a comprehensive source for private equity transactions and fund information, you may see a version of it as early as this fall.   Fund managers have joined limited partners and other industry players in supporting a global private equity database being developed by Harvard Business School professor Josh Lerner.  Graham Winfrey at Private Equity Manager reports: A group of private equity firms including Kohlberg Kravis Roberts, The Carlyle Group and Apollo Global Management have agreed to contribute transaction and fund information to a database being developed by the Private Capital Research Institution (PCRI). The…