module specification

MA6050 - Category Theory (2024/25)

Module specification Module approved to run in 2024/25
Module title Category Theory
Module level Honours (06)
Credit rating for module 15
School School of Computing and Digital Media
Total study hours 150
 
0 hours Assessment Preparation / Delivery
105 hours Guided independent study
45 hours Scheduled learning & teaching activities
Assessment components
Type Weighting Qualifying mark Description
Coursework 40%   Collection of 5 takeaway problems given weekly (individual)
Unseen Examination 60%   2-hour unseen exam
Running in 2024/25

(Please note that module timeslots are subject to change)
Period Campus Day Time Module Leader
Spring semester North Thursday Morning

Module summary

The module is designed to be an introduction to Category Theory. Category theory takes a holistic approach when dealing with objects with arrows linking them, while set theory looks at the individual elements and how the mappings effect each element between sets. Instead of focusing on different elements that hold a given structure, category theory focuses on emphasising the morphisms/actions between the objects.
Categories express abstractions of other mathematical concepts. Abstraction recognises specific situations and common features between objects.

Syllabus

Categories: Definitions, types and examples. (LO1)
Epic arrow, onto function; Monic arrow, 1-1 function, Equalisers and Co-equalisers
Initial and Terminal Objects, Products and Co-products, Duality,Limits and Co-limits, Pull-backs and Push-outs, Exponentiations. (LO2)
Subobject, Subobject Classifier, True, False, Negation, Logical Connectives. (LO3)

Balance of independent study and scheduled teaching activity

The module will be taught in 3-hour blocks divided into 1-hour lecture and 2-hour tutorial. Tutorials will be used for open discussion of the main topics covered in lectures. Students will be asked to read relevant material beforehand and offer their understanding during the tutorials. In addition to standard VLE presence there will be links available for further readings and discussion groups.

Learning outcomes

LO1: Understand the main definitions in Category Theory and link categories to different structures encountered in previous study.
LO2: Understand different actions and their compositions.
LO3: Apply language of categories to Classical Logic (Topoi).

Bibliography

Core Text:
Goldblatt, R.; Topoi: the Categorial Analysis of Logic, Dover Publications, Inc. 2006, ISBN 0486450260.
Recommended Reading:
Badiou, A., Bartlett, A. and Ling, A., n.d. Mathematics Of The Transcendental. Bloomsbury.