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What are applications of monads in general topology?

For example, for GT is important the notion of products, products are adjoints, so adjoints may be important for GT, but what's about monads?

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Any time you have an adjoint pair, you get a monad and a comonad, so if you accept that adjoints are important, maybe you can see why (co)monads may be important too... –  SL2 Jun 3 '12 at 14:51
    
@SL2: As for now the only advanced categorical notion related with my current research are products. I don't see how may I apply adjoints and monads in my research. BTW, I have the following obstacle: I have defined several different products, but don't know how exactly these are related with categorical direct products. –  porton Jun 3 '12 at 14:53
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As Sl2 said, adjoint pairs give rise to monads (and conversely, every monad gives rise to an adjoint pair of functors). These objects are ubiquitous in topology. The modern approach to homotopy theory relies on a categorical framework, and many theorems are framed in this language. –  rotskoff Jun 3 '12 at 15:55
    
@rotskoff: Homotopy is from algebraic topology while I ask about general topology. It was said that monads are important, but my question what are applications of monads is yet not answered. –  porton Jun 3 '12 at 16:48
    
As everybody knows, a topological space is nothing more than a relational $\beta$-module, where $\beta$ is the ultrafilter monad... :p –  Zhen Lin Jun 3 '12 at 16:49

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