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15
votes
29answers
722 views

Formalizations of category theory in proof assistants

What are the existing formalizations of category theory in proof assistants? I'm primarily interested in public-domain code implementing category theory in a proof assistant (Coq, Agda, ...
1
vote
2answers
447 views

How to interpret conflicting formal proofs about “a mod 0 = ? ”

The proof assistants Coq and Isabelle give conflicting formal proofs about $a \mod 0 \qquad \forall a \in \mathbb{Z}$. According to Coq $$ a \mod 0 = 0$$ and Isabelle proves $$ a \mod = a$$ ...
2
votes
0answers
853 views

Why should I trust Coq when assumption-free proof of False in Coq exists? [closed]

Damien Pous announced code for assumption-free proof of False in Coq which means inconsistency in Coq (without using exploits, lol). Damien is critical of "fully certified decision procedure ...
10
votes
4answers
1k views

Proof strength of Calculus of (Inductive) Constructions

This is a follow-on from this question, where I pondered the consistency strength of Coq. This was too broad a question, so here is one more focussed. Rather, two more focussed questions: I've ...