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(infinity,1)-monad

Idea

The notion of $(\mathrm{\infty },1)$-monad is the vertical categorification of that of monad from the context of categories to that of (∞,1)-categories.

Related concepts

• algebraic theory / Lawvere theory / (∞,1)-algebraic theory

• monad / 2-monad/ doctrine / $(\mathrm{\infty },1)$-monad

  • modal type theory

• operad / (∞,1)-operad

References

A related entry is higher monadic descent. For a comprehensive treatment of $(\mathrm{\infty },1)$-monads see Section 3 of

• Jacob Lurie, Noncommutative algebra, math.CT/0702299