@potsukichi.bsky.social
Analogy for equality vs isomorphism (with congruence):
• Equality (=): the same person
• Congruence (≡): possibly different people, but treated as the same by the rules (equal in a quotient world)
• Equality (=): the same person
• Congruence (≡): possibly different people, but treated as the same by the rules (equal in a quotient world)
January 31, 2026 at 7:03 AM
Analogy for equality vs isomorphism (with congruence):
• Equality (=): the same person
• Congruence (≡): possibly different people, but treated as the same by the rules (equal in a quotient world)
• Equality (=): the same person
• Congruence (≡): possibly different people, but treated as the same by the rules (equal in a quotient world)
A left adjoint isn’t always “free” in the intuitive sense.
For functors like Set → Vect or Set → Grp, the left adjoint really does build something “freely generated” — a free vector space or a free group. But that’s a special situation.
For functors like Set → Vect or Set → Grp, the left adjoint really does build something “freely generated” — a free vector space or a free group. But that’s a special situation.
January 17, 2026 at 9:01 AM
A left adjoint isn’t always “free” in the intuitive sense.
For functors like Set → Vect or Set → Grp, the left adjoint really does build something “freely generated” — a free vector space or a free group. But that’s a special situation.
For functors like Set → Vect or Set → Grp, the left adjoint really does build something “freely generated” — a free vector space or a free group. But that’s a special situation.
Now X (Twitter) is down?
January 16, 2026 at 3:21 PM
Now X (Twitter) is down?
Happy New Year
2026
2026
January 1, 2026 at 11:39 PM
Happy New Year
2026
2026
Hello bluesky
December 17, 2025 at 8:06 PM
Hello bluesky