A Very Short Introduction to Topos Theory (adapted from Prof. Pettigrew's notes)

TL;DR

This paper provides a concise overview of topos theory and category theory concepts, covering fundamental structures, definitions, and properties essential for understanding topos theory.

Contribution

It offers a simplified, adapted introduction to topos theory based on university notes, making complex concepts accessible for newcomers.

Findings

Clarifies key topos theory concepts

Summarizes category theory structures

Provides foundational definitions and properties

Abstract

A quick overview of category theory and topos theory including slice categories, monics, epics, isos, diagrams, cones, cocones, limits, colimits, products and coproducts, pushouts and pullbacks, equalizers and coequalizers, initial and terminal objects, exponential objects, subobjects, subobject classifiers, the definition of a topos, algebras of subobjects, functors, natural transformations and adjoint functors. This paper is refashioned and adopted from Richard Pettigrew's university notes.