The current experimental webpage contains the version of the Chapter 1 agda code from rebuild2/src, last checked on 14 October 2026.

Mathematical scope

One deviation from the book is that we do not assume that isAn is closed under equivalences of categories. This is not needed for anything in Chapter 1 and will become provable after having available the groupoid recognition principle from Chapter 2.

Publication selection

All mathematical Chapter 1 modules are included.

Modules

Chapter 1: The language of synthetic category theory
1.1 The basic vocabulary

Terminal

SCT.VolumeI.Chapter01.Section01.Terminal

Terms

SCT.VolumeI.Chapter01.Section01.Terms

Vocabulary

SCT.VolumeI.Chapter01.Section01.Vocabulary

1.2 Coherences

Coherence

SCT.VolumeI.Chapter01.Section02.Coherence

Naturality

SCT.VolumeI.Chapter01.Section02.Naturality

Products

SCT.VolumeI.Chapter01.Section02.Products

Whiskering

SCT.VolumeI.Chapter01.Section02.Whiskering

1.3 Equivalences of categories

Retracts

SCT.VolumeI.Chapter01.Section03.Retracts

Squares

SCT.VolumeI.Chapter01.Section03.Squares

Supporting

SCT.VolumeI.Chapter01.Section03.Supporting

Identifications

FunctorCoherence

SCT.VolumeI.Chapter01.Section03.Identifications.FunctorCoherence

Inverses

SCT.VolumeI.Chapter01.Section03.Identifications.Inverses

OverBase

SCT.VolumeI.Chapter01.Section03.Identifications.OverBase

Triangles

SCT.VolumeI.Chapter01.Section03.Identifications.Triangles

Products

Equivalences

SCT.VolumeI.Chapter01.Section03.Products.Equivalences

Pairing

SCT.VolumeI.Chapter01.Section03.Products.Pairing

1.4 Mapping animae

Coherence

SCT.VolumeI.Chapter01.Section04.Coherence

Core

SCT.VolumeI.Chapter01.Section04.Core

Currying

SCT.VolumeI.Chapter01.Section04.Currying

Points

SCT.VolumeI.Chapter01.Section04.Points

Uncurrying

SCT.VolumeI.Chapter01.Section04.Uncurrying

1.5 Initial categories and coproducts

Copairing

SCT.VolumeI.Chapter01.Section05.Copairing

Coproducts

SCT.VolumeI.Chapter01.Section05.Coproducts

Initial

SCT.VolumeI.Chapter01.Section05.Initial

1.6 Pullbacks of categories

Cones

SCT.VolumeI.Chapter01.Section06.Cones

Embeddings

SCT.VolumeI.Chapter01.Section06.Embeddings

Pullbacks

SCT.VolumeI.Chapter01.Section06.Pullbacks

1.7 Functor categories

CoreOfFun

SCT.VolumeI.Chapter01.Section07.CoreOfFun

Currying

SCT.VolumeI.Chapter01.Section07.Currying

Evaluation

SCT.VolumeI.Chapter01.Section07.Evaluation

1.8 Pushout squares

Cocones

SCT.VolumeI.Chapter01.Section08.Cocones

1.9 Categories over a base