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Archive for December, 2015

It’s common to think of monads as generalized algebraic theories; the most familiar examples, such as the monads on \text{Set} encoding groups, rings, and so forth, have this flavor. However, this intuition is really only appropriate for certain monads (e.g. finitary monads on \text{Set}, which are the same thing as Lawvere theories).

It’s also common to think of monads as generalized monoids; previously we discussed why this was a reasonable thing to do.

Today we’ll discuss a different intuition: monads are (loosely) categorifications of idempotents.

(more…)

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