Comments for Dan Marsden https://stringdiagram.com Theoretical computer scientist and lover of of monads and string diagrams Sun, 25 Feb 2024 10:27:58 +0000 hourly 1 http://wordpress.com/ Comment on Eilenberg-Moore Algebras by An application of monadicity – Dan Marsden https://stringdiagram.com/2022/05/20/eilenberg-moore-algebras/comment-page-1/#comment-168 Sun, 25 Feb 2024 10:27:58 +0000 http://stringdiagram.com/?p=169#comment-168 […] monadic, meaning the Eilenberg-Moore category of is equivalent to . Put another way, is monadic over . Aside from being a rather startling […]

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]]> Comment on The Continuation Monad by An application of monadicity – Dan Marsden https://stringdiagram.com/2022/11/21/the-continuation-monad/comment-page-1/#comment-167 Sun, 25 Feb 2024 10:27:55 +0000 http://stringdiagram.com/?p=2099#comment-167 […] abstract version of this proof before, as this is a special case of the adjunction that induces the continuation monad, in this case for the […]

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]]> Comment on Beck’s Monadicity Theorem by An application of monadicity – Dan Marsden https://stringdiagram.com/2024/01/21/becks-monadicity-theorem/comment-page-1/#comment-166 Sun, 25 Feb 2024 10:27:52 +0000 http://stringdiagram.com/?p=3031#comment-166 […] we have seen the basic ideas of monadicity, and Beck’s monadicity theorem, it’s time to look at an important application. Although the result in question belongs to […]

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]]> Comment on The Idea of Monadicity by An application of monadicity – Dan Marsden https://stringdiagram.com/2024/01/14/the-idea-of-monadicity/comment-page-1/#comment-165 Sun, 25 Feb 2024 10:27:49 +0000 http://stringdiagram.com/?p=3007#comment-165 […] we have seen the basic ideas of monadicity, and Beck’s monadicity theorem, it’s time to look at an important application. Although […]

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]]> Comment on What is a monad? by A monad is just a one object enriched category – Dan Marsden https://stringdiagram.com/2022/05/17/what-is-a-monad/comment-page-1/#comment-164 Sun, 04 Feb 2024 10:01:03 +0000 http://stringdiagram.com/?p=48#comment-164 […] data satisfies exactly the axioms such that is a monad. That […]

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]]> Comment on Strong Monads by A monad is just a one object enriched category – Dan Marsden https://stringdiagram.com/2022/05/30/strong-monads/comment-page-1/#comment-163 Sun, 04 Feb 2024 10:01:02 +0000 http://stringdiagram.com/?p=581#comment-163 […] that for a monoidal category , a –enriched category, or -category is a generalisation of ordinary categories […]

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]]> Comment on Bicategories, monoids, internal and enriched categories by A monad is just a one object enriched category – Dan Marsden https://stringdiagram.com/2022/10/16/bicategories-monoids-internal-and-enriched-categories/comment-page-1/#comment-162 Sun, 04 Feb 2024 10:01:00 +0000 http://stringdiagram.com/?p=1719#comment-162 […] have seen that the notion of monad can be interpreted in any bicategory. The aim of todays post is to explain that for a bicategory , a monad in is the same thing as a […]

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]]> Comment on Eilenberg-Moore limits and colimits by Algebras are regular quotients of free algebras – Dan Marsden https://stringdiagram.com/2024/01/07/eilenberg-moore-limits-and-colimits/comment-page-1/#comment-161 Sun, 28 Jan 2024 10:51:31 +0000 http://stringdiagram.com/?p=2957#comment-161 […] conclude we have a coequalizer in the Eilenberg-Moore category. Recall that the forgetful functor creates colimits that are preserved by and . As contractible coequalizers are absolute colimits, we can apply this […]

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]]> Comment on Beck’s Monadicity Theorem by Algebras are regular quotients of free algebras – Dan Marsden https://stringdiagram.com/2024/01/21/becks-monadicity-theorem/comment-page-1/#comment-160 Sun, 28 Jan 2024 10:51:28 +0000 http://stringdiagram.com/?p=3031#comment-160 […] Therefore these three morphisms form a reflexive pair. […]

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]]> Comment on The Eilenberg-Moore Adjunction by Algebras are regular quotients of free algebras – Dan Marsden https://stringdiagram.com/2022/05/20/the-eilenberg-moore-adjunction/comment-page-1/#comment-159 Sun, 28 Jan 2024 10:51:25 +0000 http://stringdiagram.com/?p=203#comment-159 […] the action of the free algebra functor, this is a pair of […]

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