infinity category

Let be a simplicial set.
Then is said to be an -category if it has the extension property for all inner horn inclusions

for

It seems reasonable to name as

1. infinity category, if one thinks about it in the context of the infinity category of infinity categories
   
2. quasicategory, if one thinks about it in the -category category of Quasicategories
   

But I'm not consistent :/