Hoysala temple architecture is a distinctive style of temple architecture that developed during the rule of the Hoysala Empire in Karnataka, India, from the 11th to the 14th century. It is known for its unique blend of Dravidian and Nagara architectural styles, intricate carvings, and exquisite craftsmanship.

Let's analyze the given statements:

1. It coexisted with the architectural works of the Mughals: Incorrect
Hoysala temple architecture predates the Mughal era in India. The Hoysala Empire flourished from the 11th to the 14th century, while the Mughal Empire emerged in the 16th century. Therefore, the Hoysala temple architecture did not coexist with the architectural works of the Mughals.

2. The exterior walls having been built using granite, these temples lack ornamentation and decoration: Incorrect
One of the defining features of Hoysala temple architecture is its intricate ornamentation and decoration. While the exterior walls of the temples are indeed made of granite, they are adorned with elaborate sculptures, friezes, and intricate carvings depicting various mythological and religious themes. The temples are replete with intricate details and decorative elements, showcasing the exquisite craftsmanship of the artisans.

Therefore, both statements are incorrect.

Hoysala temple architecture is renowned for its unique style and intricate carvings. The temples typically consist of a sanctum sanctorum (garbhagriha), a closed hall (sukanasi), an open hall (mantapa), and an entrance porch (mukhamantapa). The outer walls of the temples are adorned with intricate carvings of gods, goddesses, celestial beings, mythical creatures, and scenes from Hindu epics like the Ramayana and Mahabharata.

The sculptures are known for their lifelike expressions, intricate detailing of jewelry and costumes, and delicate workmanship. The pillars of the temples are also elaborately carved and exhibit a high level of craftsmanship. The ceilings of the mantapa and sukanasi are adorned with decorative motifs and geometric patterns.

In addition to the exquisite carvings, the temples also feature intricate lathe-turned pillars, miniature shrines, and decorative brackets known as salabhanjikas. These elements contribute to the overall beauty and grandeur of the Hoysala temple architecture.

In conclusion, Hoysala temple architecture is known for its intricate ornamentation and decorative elements. It predates the Mughal era and is a distinct style that flourished during the Hoysala Empire. It is a testament to the rich cultural heritage and architectural prowess of the Hoysala dynasty.