Skip to content

EP-0113: Categorical Morphisms, Kleisli Composition & Operads

Field Value
EP 0113
Title Categorical Morphisms, Kleisli Composition & Operads
Author Eran Rivlis & Antigravity
Status Final
Type Standards Track
Created 2026-08-01
Updated 2026-08-01

Abstract

This proposal specifies algebrax.category, building upon SparseChainComplex (EP-0101). It formalizes category-theoretic abstractions in algebrax, introducing Kleisli Composition \(g \circ_T f\) for effectful monadic morphisms as semiring matrix multiplication, providing a multi-input/multi-output Operad & String Diagram Wiring Engine, and implementing left and right Kan Extensions over sparse categories.

Deliverables

  1. Core Implementation: src/algebrax/category.py (Kleisli, compose_morphisms, kan_extension, operad_wire).
  2. Unit Tests: tests/algebrax/test_category.py (verifying monad laws, composition identity, and associative Kan extensions).
  3. Use Case Recipe: recipes/categorical_kleisli_monads.py & .ipynb.
  4. Graphical Laboratory View: View 24 (view_categorical_monads_group) in recipes/lab.py.