Print Email Facebook Twitter A computer-checked library of category theory Title A computer-checked library of category theory: Defining functors and their algebras Author Todorov, Rado (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Ahrens, B.P. (mentor) Escot, L.F.B. (mentor) Liang, K. (graduation committee) Degree granting institution Delft University of Technology Programme Computer Science and Engineering Project CSE3000 Research Project Date 2023-06-27 Abstract Category theory is a branch of abstract mathematics that aims to give a high-level overview of relations between objects. Proof assistants are tools that aid in verifying the correctness of mathematical proofs. To reason about category theory using such assistants, fundamental notions have to be defined. Computer-checked libraries contain all relevant structures and theorems in an accessible way for end users. However, current libraries of category theory are not welcoming to people without in-depth domain knowledge. This paper introduces a library of category theory tailored towards newcomers to the field as well as the learning journey of the authors. We describe the project’s structure, design choices and provide examples of the main features. Moreover, a detailed overview is provided of F-algebras and their relation with inductive data types found in functional programming languages. Construction and evaluation of types like lists and binary trees can be defined in terms of algebras. They provide a general framework for recursion over these types which allow us to reason about them with simple functions. Subject Category theoryFunctional ProgrammingProof assistant To reference this document use: http://resolver.tudelft.nl/uuid:526ed078-f8be-4a3e-a711-e5729082a589 Part of collection Student theses Document type bachelor thesis Rights © 2023 Rado Todorov Files PDF CSE3000_Final_Paper_Rado_ ... odorov.pdf 260.5 KB Close viewer /islandora/object/uuid:526ed078-f8be-4a3e-a711-e5729082a589/datastream/OBJ/view