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Tagged with monads reference-request
7 questions with no upvoted or accepted answers
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Reciprocity for algebra objects in two algebraic categories
I think this question Compact Hausdorff and C^*-algebra "objects" in a category. shows that there is no reciprocity between categories of algebra-objects of two algebraic categories.
So, ...
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6
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Original reference for the correspondence between commutative algebraic theories and commutative monads
Commutative algebraic theories were introduced by Linton in the 1966 paper Autonomous Equational Categories. Commutative monads were introduced by Kock in the 1970 paper Monads on symmetric monoidal ...
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5
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Monads which are monoidal and opmonoidal
Do monads which are monoidal and opmonoidal have a name? (Bimonoidal?) In case they have already been studied, who can point me to a reference?
More in detail. Let $(C,\otimes)$ be a symmetric (or ...
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3
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Lax morphism classifiers via lax-idempotentification
Let $T$ be a 2-monad on a nice 2-category $\mathcal K$, so that the inclusion $T\text{-}\mathbf{Alg}_s \to T\text{-}\mathbf{Alg}_l$ of the 2-category of (strict) $T$-algebras and strict $T$-algebra ...
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3
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Lax algebras for pseudomonads and monads in Kleisli bicategories for the induced pseudocomonad
In Day–Street's Lax monoids, pseudo-operads, and convolution, they remark without proof:
There are general principles involved here. Suppose $(T, m, j)$ is a pseudomonad on any bicategory $\mathcal K$...
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2
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Free commutative monoid monad
Has the monad induced by the free commutative monoid functor already been studied anywhere? Does it have any particular properties (other than not being cartesian)?
I would prefer a reference on ...
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Beck's original formulation of the precise tripleability theorem. Reference when considering reflexive pairs?
Thanks to MO's user Varkor, we have access to Beck's original untitled manuscript where Beck first stated his precise tripleability theorem. Up to terminological isomorphism, the PTT as stated in p. 3 ...
