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Results tagged with ct.category-theory
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user 1384
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
22
votes
5
answers
2k
views
are quotients by equivalence relations "better" than surjections?
This might be a load of old nonsense.
I have always had it in my head that if $f:X\to Y$ is an injection, then $f$ has some sort of "canonical factorization" as a bijection $X\to f(X)$ followed by an …
- 41.4k
10
votes
3
answers
1k
views
Are inclusions "canonical" injections?
[Background: I asked a vague question the other day, but as a result of the answers, particularly Andrej Bauer's, I now have a precise question]
Summary of question: the inclusions are a particularly …
- 41.4k
73
votes
How do I check if a functor has a (left/right) adjoint?
Lots of people-who-are-fond-of-adjoint-functor-theorems have responded to this post saying "adjoint functor theorems". Let me give a more mundane and rather different answer which fits much better int …
- 41.4k
3
votes
Splitting lemma under assumption of the axiom of choice
The mistake you're making is that your map $u$ is not a homomorphism of (whatever $A$, $B$, $C$ are---possibly groups or modules), it's just going to be a map of sets, if you define it the way you def …
- 41.4k
37
votes
Accepted
Is "all categorical reasoning formally contradictory"?
Note: I am not a historian. I'm just guessing as to what prompted the comments.
Here's my guess: if you do set theory naively, in the old-fashioned "anything is a set" way, then you run into Russell' …
- 41.4k