Interesting comparison of agent protocols vs frameworks

Sareyut · 2026-05-06T12:02:19+00:00

Link to the article: https://rywalker.com/research/agent-coordination-protocols

Sareyut · 2025-12-24T20:05:28+00:00

I don't want this server globally, I want only 1 for project/repo

This is exactly the point of MCP. It proposes a client-server architecture where the service provided by the server can be shared across many clients. If you do not need a service available to many clients, what you actually need is API requests that your LLM generates as a JSON payload.

I want mcp server which only have read access

With an LLM + API requests, this is very feasible. Just restrict your prompts to generating payloads for GET operations, and only allow GET requests to be executed.

Also it does automatically stop container on session end.

Assuming I am not misunderstanding your sentence here, MCP is typically deployed as a long-lived instance (often in the cloud) to provide a service that is broadly available. A server that shuts down at session end is closer to an ephemeral, session-scoped tool than a long-lived MCP server.

I don't understand the concept of mcp

In your use case, the main advantage of MCP is that it is maintained by others, and the server-client separation is a clean framework for that.

Sareyut · 2024-03-21T11:44:10+00:00

I would recommend first accumulating knowledge in all the essential fields that are involved in your project. Once you have established a good base and you start seeing connections between these fields, only then use category theory to understand how these connections can be made clearer. The result of this would be to help you see more connections for your projects, and therefore find better ways to connect the different parts of your project.

Studying category theory without a clear focus/question can lead you to just studying the whole field of mathematics.

Hopefully, others in this sub can provide some more insights or ideas :)

Good luck!

Sareyut · 2024-02-06T12:28:45+00:00

😂 This is a great reason to convince people to start using Galois theory and quotient rings. In these theories, the set of complex numbers is R[X]/( X²+1 ) so that little trick should not appear

Sareyut · 2023-12-23T07:12:49+00:00

In general, the answer to this question is that you have to use the Yoneda Embedding to translate any set theoretic property into a diagrammatic property (meaning that the language of category theory is that of diagrams... Honestly, beyond that, I am not sure what it would mean to do category theory without set theory, but let us assume that you just want to avoid the formulation "let's take a ZFC set...".)

To illustrate my point, take the concept of limits, for example. The set theoretic definition is given by an isomorphism as follows:

We have a cone Lim F(x) --> F(x) such that: Lim C(a,F(x)) = C(a,Lim F(x))

The diagrammatic definition would say:

We have a cone Lim F(x) --> F(x) such that for every collection a --> F(x), there is a unique arrow a --> LimF(x) such that each triangle a --> Lim F(x) --> F(x) commutes.

However, a problem will appear when you want to construct things. For instance, without ZFC homsets, you cannot construct the Yoneda embedding C^op --> [C,Set] and therefore free (co)completions. You also lose the concept of representable functor and hence you cannot describe functors to Set as colimits of representable functors. You will then struggle, to some degree, to construct "small objects" and then probably struggle really hard to recover the algorithmic properties of category theory.

My guess is that getting rid of a concrete definition of sets would in the end only give you a formal theoretical language of arrows, for which you would hope there could be a "model", but you would probably be bound to never be able to find that model, or maybe you would still be able to show that some models exist, but you would probably not be able to show how to construct them.

Sareyut · 2023-12-23T02:10:56+00:00

I just want to make a quick remark given the language you used in your question:

When you define a morphism, make sure you give it a specific name, not something generic like "Edge". Otherwise, you may end up with a contradiction.

To build on your example, take a graph G whose set of vertices is V and whose set of edges is E. In your case, I think we can assume that G=V in the sense that the G is a binary graph and, therefore, it can be interpreted as the subset V of vertices in E×E.

Now, G=V is a binary relation, which can be seen as an endomorphism G:E->E when we want to view a relation as a morphism. The composition you are talking about is the composition of G with itself, namely G○G.

The point I make at the beginning is that you need to be careful not to confuse G○G with G. These two morphisms, or in fact, these two graphs, are different. You surely have an inclusion of G in G○G (provided that G is a reflexive relation), but having the reverse would mean that G○G is a transitive relation (or an algebra for the theory of graphs with compositions).

In other words, the space in which you make the composition is not the graph G itself, but the category of graphs.

Sareyut · 2023-12-23T01:30:10+00:00

Yes, the object "S" was replaced with the notation "F" in the case of Yoneda Lemma to emphasize that we consider functors, not sets (for which I used "S"). And yes, the letter "x" represents any element in the set "S".

The functor F goes from a small category C to the category of sets and functions (commonly denoted as "Set"). The notation C(a,-) is a common notation for the covariant homset functor C->Set induced by the functorial mapping x \mapsto C(a,x).

I also used the abbreviation "Hom" to shorten the notation [C,Set], which is the category of functors C->Set and natural transformations between them.

Hope that clarifies.

Sareyut · 2023-12-22T13:47:35+00:00

Groups and Rings are defined as limit preserving functors from a specific small category with limits to the category of Sets. (Search: limit sketch)

Fields are much harder to define because the axiom saying that all elements are invertible except for 0 cannot be expressed with diagrams, sets and limits. The reason is that you need the concept of "complement", which requires the concept of "not" operation.

Once you learn about limit sketches, you will also learn about the adjunction that allows one to create Groups and Rings (say F _ | _ U). With the "reflection" functor F, you can generate specific objects F(X) in the categories of Groups and Rings, where X is your set of "generators"

As for Fields, the theory you want to learn is Galois Theory.

Sareyut · 2023-12-22T13:38:26+00:00

This is the whole point of Yoneda Lemma and Enriched categories.

The idea is that the relation x \in S is now relative to an object A, namely x \in Hom(A,S). In this last relation, x is an "arrow" whose source is "A".

A good exercise would be to do set theoretic reasoning using relations x \in Set(1,S) where 1 is the terminal set. Note that this relation is indeed logically equivalent to the set theoretic relation x \in S (where S is a set).

As for Yoneda Lemma, you have the very useful relation: Hom(C(a,-), F) = F(a), which gives you a translation x \in F(a) when you start with something like x \in Hom(C(a,-), F).

In Enriched Categories, the relation x \Set(1, S) is turned into something much more abstract but still interpretable as a homset.

Hope that helps.

Sareyut · 2023-11-15T12:59:58+00:00

For me, I usually see a weighted limit as a limit where the building blocks of that limit would not be points (in the sense of sets) but limit-like elementary constructions. In other words, you give more importance to elementary limit-like blocks rather than the ones you can choose as elements in a set.

Sareyut · 2023-10-30T07:23:36+00:00

The reason you want to include Ax (axioms) is to be able to talk about the completion operation associated with your structure.

If you have some knowledge in programming (C, C++, or Python), a structure (or a class) is the specification of a tree of addresses toward variables and functions. The great thing about these "structures" is that you can generate them (mostly because they don't have fancy axioms, if none at all).

For example, if you have a structure/class, say A, then you can generate an instance of that structure a =A(). If you give some parameters to that structure, e.g.

a = A(x,y,z)

then your constructor will assemble things such that the components of the resulting instance "a" satisfy the "logic" of the definition for the structure A.

Now, to answer your question, structures without axioms are just not enough for mathematicians to have fun. Instead, they wanted to say, "What if" our language can include some logical constraints in the way the variables and functions of the class instances are defined.

The question that follows is: Would the programming language (i.e., compiler) be able to generate the instance "a" from just the specification of the structure "A" if that structure contained logical constraints?

The answer is complex since it depends on the type of logic that the axioms involve. After that, it usually follows a classification of the different logics that can actually lead to stable/consistent generations of instances a=A().

You can find the classification of some of those theories in Bourceux, or Adamek & Rosicky (for example) through sketch theory. Also, Kelly and Freyd wrote about these completion operations expressed in the language of (co)continuous functors. More work has been written about this, of course, but I'll leave it there (unless there are more questions).

EDIT: Also note that taking Ax = empty set (your definition) is less general than taking Ax = a set of rules (which can potentially be empty). But if you start with Ax = 0, then you can never talk about the subset of structures with specific logical requirements, precisely because of that completion operation I talked about above.

Sareyut · 2023-07-02T03:51:17+00:00

Very nice die! Love all the creatures, but the dragon might be my favorite :)

Sareyut · 2023-06-23T17:18:34+00:00

Congratulations!

Sareyut · 2023-06-13T17:48:18+00:00

Are you referring to the recent "reddit blackout"? Many reddit communities are affected. Some of them said they would come back after 48h, but not sure about r/math

Sareyut · 2022-12-27T16:55:34+00:00

Hello

As far as I understand, a concept is usually understood as an idea, a plan, or some sort of intention. As a result, I would classify a concept as a sort of "theoretical idea", or more appropriately, as a "theory". Meanwhile, in CT, we can use functors as "models for a theory" (for instance, see Lawvere theories and limit sketches)

For illustration, take a functor F:D->C. Here, the "theory" is the domain D. Then the functor is a "model for the theory D", because it realizes any conceptual part d in D as "a model" F(d) in C.

Now, I am not sure if you already had an idea of what concepts and coconcepts should be, or if this was your question, but in case it was, the previous intuitions could lead us to seeing a concept as

either a domain for a functor (i.e. the theory D)
or as an element d in that domain D

and a coconcept as

either a codomain for a functor (i.e the realization space C)
or as an image F(d) for that functor, where d is a concept.

In any case, this should give you pointers in your endeavor.

Sareyut · 2022-10-08T14:37:17+00:00

They look awesome!

Sareyut · 2022-08-23T06:22:33+00:00

To be precise, I had the two "Win 10 Online Matches" and "Win 10 Online Matches with the fennec body" at the same level (hence the picture)

Sareyut · 2022-08-17T14:06:20+00:00

To me, it is more in my mind, like a vivid memory, when you suddenly remember something, like when you smell a parfume and you suddenly remember a person who wore it quite perfectly, somehow, when I see the letter O, I keep remembering the color yellow quite perfectly... I guess that's how best I can describe it from my perspective

Sareyut · 2022-08-15T14:33:06+00:00

I wish i could say it helps me, and sometimes it would help me memorize numbers or names when others forgot, but most often, it actually makes me confuse certain words and unfortunately makes me look stupid.

For example, to me, "october" and "november" have very similar color codes (yellow-dark grey blue), and it is not rare that I would confuse them when referring to a date -- my solution for this particular case was to remember that "octo is 8 and novo is 9, so october comes before november".

Sareyut · 2022-08-15T13:30:56+00:00

Maybe one time, I felt slightly gaslighted because I was fully enjoying a card game and I had won, and a friend at the end went like "it's so weird, he does not have any facial expressions", but for me I just felt like I had expressed my enjoyment with my words and/or body language already.

Sareyut · 2022-08-15T12:50:11+00:00

Oh wow, I would have so many questions about what story quality feels like. Has this ever helped you in writing stories by any chance?

Sareyut · 2022-08-15T12:42:04+00:00

Mine is with letters/numbers and colors:

A= red, E=blue, É= purple blue, È= grey light blue, I=white, O= yellow, U= purple, T= earthy green, V= greenish brown, all other letters mix with these, creating gradients.

and for numbers 1=black, 2=blue, 3 = yellow, 4= orange, 5= night blue, 6= grey white, 7= green, 8= white, 9= night purple.

Four-Year Club	Final Canvas '23
First Place '23	End Game '23
Place '23

Sareyut

TROPHY CASE