homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
An algebraic definition of ∞-groupoids and ∞-categories similar to (but older than) the definition Batanin ∞-categories.
The original definition is indicated in words in sections 1-13 of
This has been extracted and formalized in
A comprehensive account of a simplified version of the definition and its generalization from -groupoids to -categories is given in
A definition as models of a dependent type theory is given in
The relation to Batanin ∞-categories is discussed in
A brief survey is provided in
On the homotopy hypothesis for Grothendieck 3-groupoids:
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