Reputation
Next tag badge:
94/100 score
24/20 answers
Badges
2 65 139
Impact
~475k people reached

Jan
30
answered Morphisms of varieties equal over algebraic closure
Jan
29
revised Algebraic closure with no nontrival automorphism
edited tags
Jan
29
answered How do you define such map $(C^B \times B^A) \to C^A$?
Jan
29
comment The cofree coalgebra using adjoint functor theorems
In Q2, shouldn't you be looking for a weakly terminal set of objects?
Jan
29
comment The cofree coalgebra using adjoint functor theorems
I suppose it's possible in principle. If you know that $\mathbf{Coalg} (\mathcal{C})$ is $\kappa$-accessible then the $\kappa$-presentable objects form a dense subcategory. The problem is that, in the standard textbooks, no estimate of $\kappa$ is given – you have to chase through the proofs carefully. However, you might have better luck looking at the 1977 preprint of Ulmer (check your email).
Jan
29
comment How do you define such map $(C^B \times B^A) \to C^A$?
There's only one reasonable candidate: composition. And yes, you have to use evaluation and transposition.
Jan
29
answered The cofree coalgebra using adjoint functor theorems
Jan
28
comment Cohomology induces a functor
Yes. First one has to define cohomology in terms of just kernels and cokernels.
Jan
28
comment Can a Compact Lie Group have a Non-Compact Lie Subgroup?
Is it a topological embedding, however?
Jan
28
comment Adjoint to $\mathsf{Proj}$? - A quest to understand categories of graded objects.
Incidentally, the business with removing the origin is precisely why $\mathrm{Proj}$ is not functorial (with respect to graded ring homomorphisms).
Jan
28
awarded  Good Answer
Jan
28
comment Is an equivalence an adjunction?
They would have to satisfy the triangle identities if they were unit and counit for the same adjunction.
Jan
28
comment When is a functor of bicategories part of an equivalence?
Yes, there will be a pseudofunctor quasi-inverse. It's briefly mentioned in [Lack, A 2-categories companion].
Jan
28
comment Is an equivalence an adjunction?
Yes, $\epsilon$ is a counit, but not necessarily for the same adjunction.
Jan
27
answered When is a functor of bicategories part of an equivalence?
Jan
27
comment When is a functor of bicategories part of an equivalence?
It is in fact equivalent to the axiom of choice.
Jan
27
revised Why is the definition of subfunctor well-defined?
added 5 characters in body
Jan
27
comment What does “variance unity” mean?: “A normal distribution with mean $\mu$ and variance unity”.
"Unity" is sometimes a synonym for the number 1.
Jan
26
comment Matching faces in Simplicial Set theory
Yes, adjacent is a good word.
Jan
26
comment Matching faces in Simplicial Set theory
They match along lower-dimensional faces. Try drawing a picture for $n = 2$ or $n = 3$.