---
title: Topoi
description: A topos is a category that behaves like the category of sets and possesses an internal logic. Learners will understand how topoi serve as geometric spaces and alternative foundational frameworks for mathematical logic.
category: mathematics
subcategory: category-theory
difficulty: beginner, intermediate, advanced
url: /subject/topoi
---

# Topoi

A topos is a category that behaves like the category of sets and possesses an internal logic. Learners will understand how topoi serve as geometric spaces and alternative foundational frameworks for mathematical logic.

## Available Resources

1 Books • 3 Websites

## Websites

### 1. nLab: Topos

Reference article from the nLab, a research wiki maintained by working category theorists, defining Grothendieck and elementary toposes and surveying their logical and geometric interpretations. Readers get precise definitions, standard examples, and pointers to the primary literature and related entries.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ncatlab.org/nlab/show/topos

**Tags:** topos-theory, category-theory, sheaves, categorical-logic

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

### 3. nLab

Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.

**Difficulty:** Advanced | **Language:** English | **Price:** Free

**Link:** https://ncatlab.org

**Tags:** category-theory, higher-category-theory, topos-theory, homotopy-theory, reference-wiki

## Books

### 1. Topos Theory

**Author:** Peter T. Johnstone

Research-level monograph by Peter Johnstone, a principal reference for the subject, developing toposes systematically from their categorical foundations. Readers with solid category theory gain a rigorous command of elementary and Grothendieck toposes, geometric morphisms, and internal structure.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0198534256?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, category-theory

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