For someone new to all this, the generalization of a 1-category path using Batanin trees is quite fascinating—especially how one can derive source and target boundaries from any n-dimensional tree.
October 23, 2025 at 6:31 PM
For someone new to all this, the generalization of a 1-category path using Batanin trees is quite fascinating—especially how one can derive source and target boundaries from any n-dimensional tree.
Reposted by Yuri Not Igor
⚛️📝 New on Overreacted: Lean for JavaScript Developers
Lean for JavaScript Developers — overreacted
Programming with proofs.
overreacted.io
September 2, 2025 at 3:42 PM
⚛️📝 New on Overreacted: Lean for JavaScript Developers
This chart captures well why I’m digging into Applied Category Theory (#ACT). Can we aim higher without being burned by a thousand cuts? Can we avoid throwing people-power at the problem just long enough to get acquired?
August 18, 2025 at 4:20 PM
This chart captures well why I’m digging into Applied Category Theory (#ACT). Can we aim higher without being burned by a thousand cuts? Can we avoid throwing people-power at the problem just long enough to get acquired?
Reviewing my understanding of monoidal categories from this great lecture: ‘Categories for AI: Categorical Dataflow’ by Bruno Gavranović www.youtube.com/watch?v=p4iR...
Highly recommended!
Highly recommended!
Categories for AI 3: Categorical Dataflow: Optics and Lenses as data structures for backpropagation
YouTube video by Pim de Haan
www.youtube.com
August 16, 2025 at 12:14 AM
Reviewing my understanding of monoidal categories from this great lecture: ‘Categories for AI: Categorical Dataflow’ by Bruno Gavranović www.youtube.com/watch?v=p4iR...
Highly recommended!
Highly recommended!
FYI: CatColab v0.3 is out (catcolab.org/help). Here are some of the highlights:
* Petri nets as a new logic
* Migrating models between different logics
* A functional rich text editor for text cells in notebooks
* Re-organized and significantly expanded docs (catcolab.org/help)
* Petri nets as a new logic
* Migrating models between different logics
* A functional rich text editor for text cells in notebooks
* Re-organized and significantly expanded docs (catcolab.org/help)
CatColab
catcolab.org
August 6, 2025 at 8:47 PM
FYI: CatColab v0.3 is out (catcolab.org/help). Here are some of the highlights:
* Petri nets as a new logic
* Migrating models between different logics
* A functional rich text editor for text cells in notebooks
* Re-organized and significantly expanded docs (catcolab.org/help)
* Petri nets as a new logic
* Migrating models between different logics
* A functional rich text editor for text cells in notebooks
* Re-organized and significantly expanded docs (catcolab.org/help)
Fascinating how moving from 1-categories to 2-categories makes strictness optional.
But every equality you drop at one dimension has to be accounted for by new higher-dimensional equations (coherence laws) that ensure all the “up-to-isomorphism” structure still composes consistently.
But every equality you drop at one dimension has to be accounted for by new higher-dimensional equations (coherence laws) that ensure all the “up-to-isomorphism” structure still composes consistently.
July 31, 2025 at 3:17 PM
Fascinating how moving from 1-categories to 2-categories makes strictness optional.
But every equality you drop at one dimension has to be accounted for by new higher-dimensional equations (coherence laws) that ensure all the “up-to-isomorphism” structure still composes consistently.
But every equality you drop at one dimension has to be accounted for by new higher-dimensional equations (coherence laws) that ensure all the “up-to-isomorphism” structure still composes consistently.
Time to raise the semantic level from 1D semantics, which give you models like sets with operations, to 2D semantics, which give you models like categories with structure.
July 22, 2025 at 8:09 PM
Time to raise the semantic level from 1D semantics, which give you models like sets with operations, to 2D semantics, which give you models like categories with structure.
Reposted by Yuri Not Igor
Another very interesting paper directly in my area of interest is "Towards a Unified Theory of Time-Varying Data" (https://arxiv.org/pdf/2402.00206 ).
July 15, 2025 at 10:38 PM
Another very interesting paper directly in my area of interest is "Towards a Unified Theory of Time-Varying Data" (https://arxiv.org/pdf/2402.00206 ).
Shout-out to Sheaf Theory Through Examples by Daniel Rosiak. My studies over the past few weeks laid the groundwork, but this PDF was exactly what I needed at just the right moment.
https://arxiv.org/pdf/2012.08669
https://arxiv.org/pdf/2012.08669
July 14, 2025 at 9:48 PM
Shout-out to Sheaf Theory Through Examples by Daniel Rosiak. My studies over the past few weeks laid the groundwork, but this PDF was exactly what I needed at just the right moment.
https://arxiv.org/pdf/2012.08669
https://arxiv.org/pdf/2012.08669
It’s fascinating in category theory how morphisms take center stage, while objects recede to the background. Objects seem to exist merely to name the source and target of arrows. At the end of the day, the only thing that matters is that these arrow meeting points agree.
July 11, 2025 at 7:32 PM
It’s fascinating in category theory how morphisms take center stage, while objects recede to the background. Objects seem to exist merely to name the source and target of arrows. At the end of the day, the only thing that matters is that these arrow meeting points agree.
It took me a while, with many long and interesting tangents, but I think I’ve finally scratched the surface of what it means to bootstrap category theory with category theory. Tonight, I reached the “theory–model” fixpoint by bootstrapping a 1-category with itself.
July 11, 2025 at 4:32 AM
It took me a while, with many long and interesting tangents, but I think I’ve finally scratched the surface of what it means to bootstrap category theory with category theory. Tonight, I reached the “theory–model” fixpoint by bootstrapping a 1-category with itself.
Reposted by Yuri Not Igor
In the continuing saga of surprising things users do: This post over on LinkedIn features a custom made #LeanLang environment intended to replace a Jupyter Notebook, because, you know - why not? 👀
www.linkedin.com/posts/philip...
(With apologies to @jupyter.org ❤️)
www.linkedin.com/posts/philip...
(With apologies to @jupyter.org ❤️)
[New Blog Post] Doing Lean Dirty: Lean as a Jupyter Notebook Replacement https://lnkd.in/ejy9hE5z #lean4 | Philip Zucker
[New Blog Post] Doing Lean Dirty: Lean as a Jupyter Notebook Replacement https://lnkd.in/ejy9hE5z #lean4
www.linkedin.com
July 8, 2025 at 9:43 PM
In the continuing saga of surprising things users do: This post over on LinkedIn features a custom made #LeanLang environment intended to replace a Jupyter Notebook, because, you know - why not? 👀
www.linkedin.com/posts/philip...
(With apologies to @jupyter.org ❤️)
www.linkedin.com/posts/philip...
(With apologies to @jupyter.org ❤️)
Reposted by Yuri Not Igor
📣 We're excited to share the new lean-lang.org!
Relaunching our website was a key deliverable in our Year 2 roadmap to provide "improved navigation and access to valuable content, resources, and tools." We hope you like it!
#LeanLang #LeanProver
Relaunching our website was a key deliverable in our Year 2 roadmap to provide "improved navigation and access to valuable content, resources, and tools." We hope you like it!
#LeanLang #LeanProver
July 7, 2025 at 9:02 PM
📣 We're excited to share the new lean-lang.org!
Relaunching our website was a key deliverable in our Year 2 roadmap to provide "improved navigation and access to valuable content, resources, and tools." We hope you like it!
#LeanLang #LeanProver
Relaunching our website was a key deliverable in our Year 2 roadmap to provide "improved navigation and access to valuable content, resources, and tools." We hope you like it!
#LeanLang #LeanProver
Reposted by Yuri Not Igor
📣 #LeanLang v4.21 is released! This release brings 295 changes, including feature additions, bug fixes, refactors, documentation improvements and performance improvements, in support of our Y2 roadmap: lean-fro.org/about/roadma...
➡️ See the full changelog here: lean-lang.org/doc/reference/
➡️ See the full changelog here: lean-lang.org/doc/reference/
June 30, 2025 at 8:22 PM
📣 #LeanLang v4.21 is released! This release brings 295 changes, including feature additions, bug fixes, refactors, documentation improvements and performance improvements, in support of our Y2 roadmap: lean-fro.org/about/roadma...
➡️ See the full changelog here: lean-lang.org/doc/reference/
➡️ See the full changelog here: lean-lang.org/doc/reference/
Loving @nonzerosumjames.bsky.social's Non-Zero-Sum James podcast! It really lives up to the name — a true non-zero-sum experience with a high signal-to-noise ratio. A small investment of time for excellent content.
June 28, 2025 at 3:40 PM
Loving @nonzerosumjames.bsky.social's Non-Zero-Sum James podcast! It really lives up to the name — a true non-zero-sum experience with a high signal-to-noise ratio. A small investment of time for excellent content.
Been modeling a transaction log using category theory — with functors, natural transformations, and (believe it or not) slice categories.
June 27, 2025 at 1:54 PM
Been modeling a transaction log using category theory — with functors, natural transformations, and (believe it or not) slice categories.
Yet another category theory paper — but this one actually starts to make sense. At least I finally have the buckets in my head to stuff the notions I read into…
A Graphical Theory of Monads by Jirka Maršík & Dusko Pavlovic
stringdiagram.com/wp-content/u...
A Graphical Theory of Monads by Jirka Maršík & Dusko Pavlovic
stringdiagram.com/wp-content/u...
stringdiagram.com
June 27, 2025 at 1:42 PM
Yet another category theory paper — but this one actually starts to make sense. At least I finally have the buckets in my head to stuff the notions I read into…
A Graphical Theory of Monads by Jirka Maršík & Dusko Pavlovic
stringdiagram.com/wp-content/u...
A Graphical Theory of Monads by Jirka Maršík & Dusko Pavlovic
stringdiagram.com/wp-content/u...
I just realized something—obvious in hindsight: equations in a category also generalize over cells of any dimension, which is beautiful.
June 25, 2025 at 7:16 PM
I just realized something—obvious in hindsight: equations in a category also generalize over cells of any dimension, which is beautiful.
Coming from software development, Category Theory can initially feel like a step backward — a dense wall of abstract concepts that seem to merely describe what we already do intuitively when building software.
June 20, 2025 at 2:41 PM
Coming from software development, Category Theory can initially feel like a step backward — a dense wall of abstract concepts that seem to merely describe what we already do intuitively when building software.
When does a logic stops being a language specification and starts being a logic programming language?
June 19, 2025 at 1:54 PM
When does a logic stops being a language specification and starts being a logic programming language?
Learning by going back in time with Goguen at al ...
cseweb.ucsd.edu
June 15, 2025 at 10:17 PM
Learning by going back in time with Goguen at al ...
Re-reading ‘Algebraic Model Management: A Survey’ (arxiv.org/pdf/2301.04846) and I come across: “An instance I on schema S is a theory extending S with new 0-ary
function (constant) symbols called generators and non-quantified equations.”
function (constant) symbols called generators and non-quantified equations.”
arxiv.org
June 14, 2025 at 3:37 PM
Re-reading ‘Algebraic Model Management: A Survey’ (arxiv.org/pdf/2301.04846) and I come across: “An instance I on schema S is a theory extending S with new 0-ary
function (constant) symbols called generators and non-quantified equations.”
function (constant) symbols called generators and non-quantified equations.”
Just read about a fascinating breakthrough in computational complexity from Ryan Williams. He's made what's been called "an earthquake of a result" by figuring out how to dramatically reduce the memory (computational space) a program uses.
June 13, 2025 at 1:03 PM
Just read about a fascinating breakthrough in computational complexity from Ryan Williams. He's made what's been called "an earthquake of a result" by figuring out how to dramatically reduce the memory (computational space) a program uses.
Reading “GATlab: Modeling and Programming with Generalized Algebraic Theories” (entics.episciences.org/14666/pdf) for a second time after a stroll around algebraic theories, model theory.
entics.episciences.org
June 9, 2025 at 5:10 PM
Reading “GATlab: Modeling and Programming with Generalized Algebraic Theories” (entics.episciences.org/14666/pdf) for a second time after a stroll around algebraic theories, model theory.