1 Introduction

This chapter contains some general information about the Clowder Project.

• Section 1.1: Introduction
  • Subsection 1.1.1: Project Description and Goals
    • Subsubsection 1.1.1.1: Provide a Unified and Complete Reference for Category Theory
    • Subsubsection 1.1.1.2: Gather Hard to Find Results
    • Subsubsection 1.1.1.3: Elaborate on Details That Are Often Left Out
    • Subsubsection 1.1.1.4: Homogenize Conventions, Notation, and Terminology
    • Subsubsection 1.1.1.5: Fill Gaps in the Category Theory Literature
    • Subsubsection 1.1.1.6: Provide a Citable Reference for All Kinds of Results
  • Subsection 1.1.2: Navigating the Clowder Project
    • Subsubsection 1.1.2.1: Preferences
    • Subsubsection 1.1.2.2: Large Diagrams and the Zoom in Feature
    • Subsubsection 1.1.2.3: PDF Styles
  • Subsection 1.1.3: Prerequisites/Assumed Background
  • Subsection 1.1.4: Community Engagement, Contributions and Collaboration
    • Subsubsection 1.1.4.1: How to Contribute
    • Subsubsection 1.1.4.2: Ways to Contribute: Missing Proofs
    • Subsubsection 1.1.4.3: Ways to Contribute: Missing Examples
    • Subsubsection 1.1.4.4: Ways to Contribute: Questions
  • Subsection 1.1.5: Frequently Asked Questions
    • Subsubsection 1.1.5.1: How does Clowder differ from the nLab?
    • Subsubsection 1.1.5.2: Why not just use the nLab instead?
  • Subsection 1.1.6: Goodies
    • Subsubsection 1.1.6.1: General Utility
    • Subsubsection 1.1.6.2: Set Theory Through a Categorical Lens
    • Subsubsection 1.1.6.3: Category Theory
• Section 1.2: Project Overview
  • Subsection 1.2.1: Content and Scope
    • Subsubsection 1.2.1.1: Elementary Category Theory
    • Subsubsection 1.2.1.2: Variants of Category Theory
    • Subsubsection 1.2.1.3: Higher Category Theory
    • Subsubsection 1.2.1.4: $\infty $-Categories
    • Subsubsection 1.2.1.5: Other Topics
  • Subsection 1.2.2: Style
    • Subsubsection 1.2.2.1: Presentation of Topics
    • Subsubsection 1.2.2.2: Provable Items Come With Proofs
    • Subsubsection 1.2.2.3: Proper Justification of Proofs
  • Subsection 1.2.3: Infrastructure and Technical Implementation
    • Subsubsection 1.2.3.1: Removed Features (in Comparison With the Stacks Project)
    • Subsubsection 1.2.3.2: Gerby and the Tags System
    • Subsubsection 1.2.3.3: Placeholder Symbols and Future Style
• Section 1.3: Lists
  • Subsection 1.3.1: List of Omitted Proofs
    • Remark 1.3.1.1.1: Omitted Proofs To Add
  • Subsection 1.3.2: List of Missing Examples
    • Remark 1.3.2.1.1: Missing Examples to Add
  • Subsection 1.3.3: List of Questions
    • Remark 1.3.3.1.1: Questions to Answer
  • Subsection 1.3.4: List of Gaps in the Category Theory Literature
    • Gap 1.3.4.1.1: The Tensor Product of Presentable Categories
    • Gap 1.3.4.1.2: Explicit Descriptions of Co/Limits of Categories
    • Gap 1.3.4.1.3: Dinatural Transformation Co/Classifiers
    • Gap 1.3.4.1.4: The Tensor Product of Symmetric Monoidal Categories
    • Gap 1.3.4.1.5: A Comprehensive Treatment of the Theory of Promonoidal Categories
    • Gap 1.3.4.1.6: A Comprehensive Treatment of the Theory of Multicategories
    • Gap 1.3.4.1.7: A Compendium of Examples of 2-Categorical Notions
    • Gap 1.3.4.1.8: Centres and Traces of Categories
    • Gap 1.3.4.1.9: Natural Cotransformations
    • Gap 1.3.4.1.10: A Comprehensive Treatment of Isbell Duality
    • Gap 1.3.4.1.11: A Comprehensive Theory of 2-Dimensional Co/Ends
    • Gap 1.3.4.1.12: A Comprehensive treatment of Factorisation Systems
    • Gap 1.3.4.1.13: Proofs of Coherence Theorems for String Diagrams
    • Gap 1.3.4.1.14: A Comprehensive Treatment of Variants of Category Theory