Overview

This Agda code accompanies our CSL 2025 paper Coslice Colimits in Homotopy Type Theory. It has been checked with Agda 2.6.4.3.

Organization

• HoTT-Agda/

  A stripped down version of Andrew Swan's HoTT-Agda branch, with local changes for general lemmas we proved during the development.

  It also includes a proof of the 2-coherence of the Suspension-Loop adjunction and some properties of homogeneous types (used for the proof of 2-coherence).

  See HoTT-Agda/README.md for the license of the work inside this directory.

• Colimit-code/

  Our formalization of our construction of an A-colimit.

  See Colimit-code/README.md for details and for the license of the work inside this directory.

• Pullback-stability/

  Our formalization of pullback stability (or universality) for all ordinary colimits.

  See Pullback-stability/README.md for details and for the license of the work inside this directory.

Type-checking with Docker

NOTE: We have successfully tested the following Docker container on Linux but not on other operating systems.

1. Build Docker image:

   docker build . -t colimit

   The building itself type checks the whole development. The type-checking is partitioned into multiple stages, for otherwise the type-checking could take an unacceptably long time. The entire build may take over an hour. The type-checking of all our Agda code takes about 23 minutes on our host Ubuntu.

2. Generate HTML files:

   mkdir -p ./html1 ./html2
   docker run --mount type=bind,source=./html1,target=/build/Colimit-code/html \
     --mount type=bind,source=./html2,target=/build/Pullback-stability/html \
     colimit

   The HTML files will be under html1/ and html2/. The entry points will be

   • html1/CosColim-Adjunction.html
   • html2/Stability.html

Acknowledgement

This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-21-1-0009. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force.