Ganesha too has various forms.
Ganapati - the Lord of ‘Ganas’ which means attendants. These attendants are:
(a) In the Macrocosm - the elements, elemental beings, demi-semi-gods of various categories, etc. Ganesha gives mastery over these beings as well, if his energy is accessed. A lot of times, these beings also cause mischief, and he prevents such occurrences.
(b) In the Microcosm - these represent the senses (eyes, ears, nose, skin, taste) and he has complete mastery over them so that one can turn inward. Without these obstacles, one can jump deep into meditation and contemplation.
This form of Ganesha propitiated at the very beginning of every activity, is generally a four-handed depiction:
Mahaganapati (Great Ganapati or Ganesha) is a higher-form in which he is present with a consort - named Siddhilakshmi. This is the form we invoke in the Tantra practice because Yin-Yang always go hand in hand. We call that Yab-yum in Tibetan, with the male representing Compassion and the Female, Insight/Wisdom. In Hindu parlance, the female is Power (shakti) and the male is the holder of this Power (Shaktimaan) - neither is complete without the other.
Siddhilakshmi is the personification of perfection, or goals already accomplished, as also the bestower of property and fulfillment. His ten hands signify ten forms of blessings while his consort represents the fulfillment of what one seeks.
The Yagna covers both these aspects of the deity.