zanzi - Network

why not take a break from <recent discourse> and help me figure out what an n-ary Let binding should look like? I *think* what we need...

why not take a break from <recent discourse> and help me figure out what an n-ary Let binding should look like?
I *think* what we need to do is to use the fact that List is a monad to define a Bind for List-indexed monads? Does this sound like it's on the right track?

"are neural networks a polycategory" - the greatest paper in the history of applied category theory, rejected by reviewer n2 after...

"are neural networks a polycategory" - the greatest paper in the history of applied category theory, rejected by reviewer n2 after 12,239 pages of intricate coherence diagrams

dependent types puzzle N2: what does an n-ary Let binding look like? there's a version for linear and Cartesian contexts

dependent types puzzle N2: what does an n-ary Let binding look like?
there's a version for linear and Cartesian contexts

dependent types puzzle: how to generalise this pattern?note: Multi-functors need to form a multicategory, so "functor from product...

dependent types puzzle: how to generalise this pattern?

note: Multi-functors need to form a multicategory, so "functor from product category" does not count as an answer.

can we define a relative monad w.r.t the environment comonad? ie we would have return : w a -> m abind : m a -> (w a -> m a) ->...

can we define a relative monad w.r.t the environment comonad? ie we would have

return : w a -> m a
bind : m a -> (w a -> m a) -> m a

where 'w a' is a type of variables 'a' in an environment 'w'.

Watching the talks for ACT2023, as a category theorist I am glad that there are so many amazing tools being built in Python, Julia, etc, but...

Watching the talks for ACT2023, as a category theorist I am glad that there are so many amazing tools being built in Python, Julia, etc, but as a functional programmer I feel like FP dropped the ball by not becoming the go-to family of languages for applied category

What is the right notion of "f algebra" for double categories?Can I formulate something like an "f-algebra with...

What is the right notion of "f algebra" for double categories?
Can I formulate something like an "f-algebra with relations" where the functor part gives me the constructors of an inductive type and the profunctor gives me the relations/equations/rewrites?

is there a name for these two different ways of defining a graph?ie the definition on the left is using a set of nodes and edges with two...

is there a name for these two different ways of defining a graph?
ie the definition on the left is using a set of nodes and edges with two maps inbetween, versus defining a graph as a set of vertices and a set of edges indexed by the vertices

@JacquesC2 what do I need to do to express Pi/Sigma through comma categories? do i need to form a pullback as a product in a comma category,...

@JacquesC2 what do I need to do to express Pi/Sigma through comma categories? do i need to form a pullback as a product in a comma category, and then show the adjunction between pullback and Pi/Sigma?

first start on comma categories, we can use them to re-derive the category of algebras of an endofunctor

first start on comma categories, we can use them to re-derive the category of algebras of an endofunctor

Big if true (up to size issues)

Big if true (up to size issues)

finally going to try formalizing comma categories in Idriswhat are some interesting examples that could be worth implementing?

finally going to try formalizing comma categories in Idris

what are some interesting examples that could be worth implementing?

@julesh suggested that it would have a bi-kleisli category. Is there an analogous notion of "bi-em category"

@julesh suggested that it would have a bi-kleisli category. Is there an analogous notion of "bi-em category"

Suppose we have a functor F that's both a monad and a comonad. Can we say something about the relationship between it's (co)kleisli...

Suppose we have a functor F that's both a monad and a comonad.

Can we say something about the relationship between it's (co)kleisli and (co)EM categories?

Monads have a very rich meta-theory, but what makes them special? Can any of the meta-theory of monads be translated to other monoidal...

Monads have a very rich meta-theory, but what makes them special?

Can any of the meta-theory of monads be translated to other monoidal structures in the cat of endofunctors, ie day convolution?

the eilenberg-moore construction for an arbitrary functor using the freer algebra over that functor

the eilenberg-moore construction for an arbitrary functor using the freer algebra over that functor

is it just me or are eilenberg-moore categories not as useful in functional programming? we use kleisli categories all the time, but the...

is it just me or are eilenberg-moore categories not as useful in functional programming?

we use kleisli categories all the time, but the em-adjunction just feels kind of tautological. what am i missing?

adjoint folds? what about kan-extension folds?

adjoint folds? what about kan-extension folds?

thinking of cancelling my GPT subscription. I don't know if GPT 4 is getting worse but more and more I keep getting better responses...

thinking of cancelling my GPT subscription. I don't know if GPT 4 is getting worse but more and more I keep getting better responses from GPT 3.5

this isn't even a diss against mastodon, it's more just me realizing that id enjoy mastodon a lot more if it wasnt federated

this isn't even a diss against mastodon, it's more just me realizing that id enjoy mastodon a lot more if it wasnt federated