Malthe Sporring

I am a PhD student of Clark Barwick at the University of Edinburgh. I am interested in homotopy theory and (higher) category theory. I am also interested in theorem proving via LEAN and automated assessment via STACK. When I’m not thinking about mathematics, I may be swing dancing or bouldering.


Informal notes on various topics. Comments and corrections are welcomed.
  • png (Co)ends: a taster

    (August 2023) (Co)ends are an effective organisational tool in category theory, unifying many different concepts and providing a compact substitution to element-wise proofs. These notes are based on "Coend calculus" by Fosco Loregian.
  • png Persistent homology

    (December 2022) Notes on persistent homology, as part of a GlaMS (Glasgow-Maxwell school) group project. Joint with Yan Yau Cheng and Adrián Doña Mateo.
  • png Axiomatic homology theory

    (September 2021) Undergraduate notes on axiomatic homology theory. Homology is typically introduced as singular homology, with theorems proven explicitly using chain calculations. We take a different approach, defining a homology theory axiomatically as by Eilenberg and Steenrod, and then proving classical theorems directly from the axioms. This project was supervised by Prof. Clark Barwick and funded by the University of Edinburgh School of Mathematics Vacation Scholarship and College Vacation Scholarship funds.



Tutoring - Edinburgh

  • (Spring 2024) Honour Algebra - Skills
  • (Spring 2024) Proofs and Problem Solving
  • (Fall 2023) Category Theory
  • (Fall 2023) Honours Analysis - Skills
  • (Fall 2023) MathsBase
  • (Spring 2023) Algebraic Topology
  • (Spring 2023) Fundamentals of Pure Mathematics


  • (Fall 2023) I am mentoring a project on algebraic topology for Twoples, an online directed reading program for maths undergraduates.

Reading groups


STACK is an open source online assessment system for STEM subjects. I have been involved in STACK since 2019 - here are some of my contributions: