#categorytheory — Public Fediverse posts

While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.

#math #mathematics #topology #algebra #CategoryTheory

Readings shared April 4, 2026. https://jaalonso.github.io/vestigium/posts/2026/04/04-readings_shared_04-04-26 #AI #AI4Math #ATP #Agda #AlphaProof #Autoformalization #CategoryTheory #CoqProver #FunctionalProgramming #ITP #IsabelleHOL #LLMs #LambdaCalculus #LeanProver #Lisp #Logic #LogicProgramming #LLMs #Math #Physics #Programming #Prolog #Racket #RocqProver #Vampire

Readings shared March 09, 2026. https://jaalonso.github.io/vestigium/posts/2026/03/10-readings_shared_02-09-26 #AI #AI4Math #CategoryTheory #CoqProver #Emacs #FunctionalProgramming #Haskell #ITP #IsabelleHOL #LambdaCalculus #LeanProver #Lisp #Math #Physics #RocqProver

Differential Propositional Calculus • 10

Special Classes of Propositions (cont.)

Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.

Linear Propositions

The linear propositions, may be written as sums:

One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that

In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.

At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.

Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.

Next are the three linear propositions of rank 1, which are none other than the three basic propositions,

At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple

Resources

• Logic Syllabus
• Survey of Differential Logic

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

#Introduction

Hello folks! I'm an undergraduate student in mathematics interested in abstract homotopy theory, and category theory at large! Aside from that, in my spare time I love programming, reading books and listening some good music!

I'm also into vegetarianism, philosophy, open source, looking forward to learn more about socialism and a variety of other topics :)

#maths #categoryTheory #homotopy #programming #music #books #openSource #philosophy #vegetarian #socialism