Basic concepts
Basic theorems
homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
Applications
Models
n-category = (n,n)-category
n-groupoid = (n,0)-category
Morphisms
Functors
Universal constructions
Extra properties and structure
1-categorical presentations
Background
Basic concepts
-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
An algebraic quasi-category is a quasi-category equipped with a choice of (inner) horn fillers.
Algebraic quasi-categories give a algebraic definition of (∞,1)-categories.
For more see the section Algebraic fibrant models for higher categories at model structure on algebraic fibrant objects.