The four important Vaishnava shrines of Srirangam, Tirumala, Kanchipuram and Melkote are referred to respectively as Bhoga Mandapa, Pushpa Mandapa, Tyaga Mandapa and Jnana Mandapa.
Kanchipuram earned the name of Tyaga Mandapa because Lord Varadaraja of Kanchi gave generously to His devotees. The Acharya Ramanuja was dear to Him, but he gave him up to Ranaganatha of Srirangam so that Ramanuja could continue the work of the Vaishnava preceptor Alavandar.
In fact, because Varadaraja gave up even what was dear to Him, He is also known as Tyagaraja — the king among givers. He is like Lord Krishna in this respect. No matter how much Krishna gave to those who sought His help, He was still not satisfied and always felt that there was room for more generosity. When His avatara was about to end, Lord Krishna cried because He felt He had not done enough for Draupadi. That kindness of Krishna is seen in Lord Varadaraja too, said Akkarakkani Srinidhi in a discourse. One reason for this could be that He, more than any other deity, is more often in the company of His Consort Perundevi and it is as if Her gentleness has rubbed off on Him, although He is Himself kind hearted.
In fact, one may go so far as to say that Varadaraja is the visual representation of the Dvaya mantra, which celebrates both the Lord and His Consort. In the archa (idol) form, the Lord does not move or speak. But Lord Varadaraja of Kanchipuram used to have conversations with His devotee Thirukachi Nambi, as the latter fanned Him. Ramanuja had to debate a scholar called Yajnamurthi and Ramanuja was worried that the debate was not going in his favour. It was Varadaraja who guided Ramanuja and helped him defeat Yajnamurthi.