• Lean

  • Referenced in 45 articles [sw15148]
  • small trusted kernel based on dependent type theory. It aims to bridge the gap between ... currently being used to formalize category theory, homotopy type theory, and abstract algebra. We describe...
  • HoTT

  • Referenced in 15 articles [sw15147]
  • levels, and a significant amount of category theory centered around comma categories and functoriality ... various constructions involving comma categories. A significant amount of work has gone into ensuring that ... both of Coq and of univalent type theory, which allow our library to compile...
  • BIGEBRA

  • Referenced in 21 articles [sw00078]
  • forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures...
  • Globular

  • Referenced in 5 articles [sw18031]
  • verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher...
  • Verigraph

  • Referenced in 4 articles [sw23736]
  • approach to GT is based on category theory, allowing the instantiation of theoretical results...
  • RATH-Agda

  • Referenced in 3 articles [sw13303]
  • Theories in Agda. The basic category and allegory theory library of the RATH-Agda project ... only sporadically truly) literate theories ranging from semigroupoids, which are “categories without identities”, to “action ... typed Kleene algebras), including also monoidal categories. These theories are intended as interfaces for high...
  • diagrams.sty

  • Referenced in 2 articles [sw30360]
  • drawing so-called “commutative” diagrams in category theory and related subjects. Unlike many other packages...
  • pipes

  • Referenced in 2 articles [sw13660]
  • including dependencies; Elegant semantics: Use practical category theory; ListT: Correct implementation of ListT that interconverts...
  • Catlab

  • Referenced in 1 article [sw40951]
  • framework for applied and computational category theory, written in the Julia language. Catlab provides ... interactive interface for applications of category theory to scientific and engineering fields. It emphasizes monoidal ... categories due to their wide applicability but can support any categorical structure that is formalizable ... generalized algebraic theory...
  • AxiomaticCategoryTheory

  • Referenced in 1 article [sw32222]
  • Axiom Systems for Category Theory in Free Logic. This document provides a concise overview ... exploration of axioms systems for category theory. Extending the previous studies (http://arxiv.org/abs/1609.01493)...
  • idris-ct

  • Referenced in 1 article [sw40897]
  • idris-ct: A Library to do Category Theory in Idris. We introduce idris ... between academy and industry, catering both to category theorists who want to implement ... engineers who care about formalization with category theory: It is inspired by similar libraries developed...
  • ARTMAP

  • Referenced in 6 articles [sw03013]
  • shrink, 3) limiting a category hypervolume, 4) using Bayes’ decision theory for learning and inference...
  • Opycleid

  • Referenced in 1 article [sw31290]
  • developed and extended using elements of category theory. The API for Opycleid was designed ... very general approach to TMT by considering category actions in Rel, i.e. faithful functors from ... small category to the 2-category Rel of finite sets and relations between them ... group usually found in neo-Riemannian theory), allowing the analysis of chords with just...
  • DisCoPy

  • Referenced in 1 article [sw40949]
  • experiments in the various applications of category theory where diagrams have become a lingua franca...
  • Statebox

  • Referenced in 1 article [sw40899]
  • approach which utilizes, amongst other things, category theory, Petri nets and cryptography. You can learn...
  • CQL

  • Referenced in 1 article [sw40898]
  • combining, migrating, and evolving databases — using category theory, a branch of mathematics that has revolutionized...
  • Sheafhom 2.0

  • Referenced in 1 article [sw00854]
  • provides partial support for items from category theory as first-class objects: vector spaces, morphisms...
  • MiniBrass

  • Referenced in 1 article [sw31298]
  • Both arguments draw upon elements from category theory. MiniBrass turns these theoretical considerations into practice...
  • RoughSets

  • Referenced in 8 articles [sw31808]
  • those theories. The methods included in the package can be divided into several categories based...
  • raSAT

  • Referenced in 8 articles [sw15206]
  • solve problems in QF_NRA category, i.e., bounded quantification on conjunction of polynomial inequalities ... combines miniSAT 2.2 and background theories, which are various interval arithmetics. Main features are: raSAT...