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(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
5
votes
Constructive homological algebra in HoTT
I posted an answer citing my work with Jarl Flaten on defining Ext groups constructively at https://mathoverflow.net/a/447555/952, where I also mention that you can use this to define other derived fu …
15
votes
How to make Ext and Tor constructive?
Jarl Flaten and I have developed the theory of Ext groups constructively in homotopy type theory, and have formalized most of the results in Coq. We use Yoneda's resolution-free approach to Ext, so t …