Introduction to Categories and Categorical Logic

Details Introduction to Categories and Categorical Logic Introduction to Categories and Categorical Logic

2011-02-07

arxiv.org/abs/1102.1313v1

In New Structures for Physics, B. Coecke (ed). Lecture Notes in Physics Vol. 813, pages 3--94, Springer-Verlag 2011

Mathematics

Category Theory

96 pages

Scientific paper

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisites. The coverage is by no means comprehensive, but should provide a good basis for further study; a guide to further reading is included. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions. An Appendix contains a summary of what we will need, and it may be useful to review this first. In addition, some prior exposure to abstract algebra - vector spaces and linear maps, or groups and group homomorphisms - would be helpful.

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