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- What is it that Leibniz calls a “Monad”?
Monads capable of this are called "vernünftige Seelen" or "Geister" (intelligent souls or spirits, "animae") Now, there is a hierarchy of monads with regard to their apperceptions: From "schlummernden" (slumbering) up to the omniscient monad, the "monas monadum" (monad of monads) – God Somewhere in between are animal and spirit monads
- What is a monad in a - Mathematics Stack Exchange
Once you know this, then the usual definition of monad carries over straightforwardly at least in a strict 2-category In a weak 2-category (i e bicategory in the sense of Bénabou), because we need not have $(h \circ g) \circ f \stackrel{?}{=} h \circ (g \circ f)$ for 1-cells, one has to be a little bit more careful with the definition of
- How do monads arise in mathematics? - Mathematics Stack Exchange
It sounds like he actually introduced the notion of a comonad as opposed to a monad, and he used the term "standard construction" I'm completely guessing here since I don't have access to the article, but I suspect he was defining a comonad to organize the degeneracy and face maps of a simplicial complex or similar
- Simple explanation of a monad - Mathematics Stack Exchange
$\begingroup$ They are very much the same because a monad in Haskell is just an example of a category-theoretical monad in the category $\bf Hask$ (well, internal to Hask that is ) Its pretty much the same as $\bf Set$ though $\endgroup$ –
- Leibniz monads connection to the physical universe atom
Monad is indivisible and indestructible due to the unity (self-containment) nature As you can see, Dalton's atom is borrowed from the lemma 3 By the time Dalton was around, Leibniz's metaphysical conception of monad was far out of favor
- What are the algebras of the double powerset monad?
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- Is the powerset monad unique? - Mathematics Stack Exchange
Any hints if this monad already appears in the literature and if it has a name are appreciated Algebras for the monad This raises of course the question how to describe the algebras for this monad One can mimic the proof for the usual monad structure, where the algebras are sup-lattices, and arrive at those partially ordered sets where
- Understanding the Giry monad - Mathematics Stack Exchange
So a monad on a category $\mathbf{C}$ is basically an endofunctor on $\mathbf{C}$ together with a family of mapts $\mu_X : TTX \rightarrow TX$ that are compatible in a certain way The actual definition is a little bit more complicated; for example, we also have a monoidal unit $\eta$
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