Monads 单子(Dr. Eugenia Cheng)

Dr. Eugenia Cheng ‘s Lectures on Category Theory (2007)

1. Definition of Monad,  Example: Monad for Monoids

The name “monad” came from “monoid” and “triad”, which indicated that it is a triple (1 functor + 2 trasformations), monoidic algebraic structure.

Monad = Monoid + Triad

Monad = Monoid (restricted to endofunctors)

Note: She was annoyed nobody had corrected her mistake in (red) Tμ . (I discovered it only on 2nd revision view few years later).

2. Example2: Monad for Categories

Monad for Small Categories (= Set)

3. Algebra = Monad 



What is the difference between Monoid and Monad? (Bartosz Milewski )

Monad (图解)  : 单子
Functor: 函子


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