Reputation
2,635
Next privilege 3,000 Rep.
Cast close & reopen votes
Badges
3 27 57
Impact
~246k people reached

Jan
5
awarded  Favorite Question
Dec
26
comment Does a left Kan lift of a homset functor Hom(*, - ): C -> {Set} through the forgetful functor {M-Set} -> {Set} exist?
Thanks, pro, you suggestion has basically answered my question in the affirmative. Since $\mathsf{U}$ has a left adjoint, the required left Kan lift exists.
Dec
26
comment Does a left Kan lift of a homset functor Hom(*, - ): C -> {Set} through the forgetful functor {M-Set} -> {Set} exist?
Indeed, the functor from $\mathsf{Set}$ to $M\mathsf{Set}$ which sends a set $X$ to the $M$-set $X$ with the trivial action is left adjoint to $\mathsf{U}$.
Dec
26
comment Does a left Kan lift of a homset functor Hom(*, - ): C -> {Set} through the forgetful functor {M-Set} -> {Set} exist?
In your example, the functor $\mathrm{Hom}_{C}(p, - )$ will be the identity functor on $\mathsf{Set}$. In that case, the question is just asking whether the forgetful functor $\mathsf{U}$ has a left adjoint.
Dec
26
asked Does a left Kan lift of a homset functor Hom(*, - ): C -> {Set} through the forgetful functor {M-Set} -> {Set} exist?
Dec
19
awarded  Socratic
Dec
18
comment Is there another equivalence relation on based maps between spheres which form the same graded ring as the homotopy groups?
I'm actually hoping to see what kinds of pathological behavior can occur, and whether the isomorphisms with the usual homotopy groups of sphere are enough to constrain the relation $\sim$.
Dec
18
comment Is there another equivalence relation on based maps between spheres which form the same graded ring as the homotopy groups?
Yes, Sebestian, you are right that I need $\sim$ to be compatible with the operation $\vee$ in order that $\mathrm{Map}(S^k, S^n)/\sim $ forms a magma.
Dec
18
asked Is there another equivalence relation on based maps between spheres which form the same graded ring as the homotopy groups?
Dec
17
asked Determining finite abelian groups among algebraic theories by counting
Dec
12
awarded  Yearling
Nov
9
awarded  Popular Question
Sep
17
comment How would set theory research be affected by using ETCS instead of ZFC?
ETCS and ZFC suggest different fragments with which to do reverse mathematics.
Jun
30
awarded  Favorite Question
Jun
7
awarded  Good Question
May
26
awarded  Nice Question
Mar
9
revised Multivariate ML inequality and holomorphic functions on the closed unit ball
added 204 characters in body
Mar
9
revised Multivariate ML inequality and holomorphic functions on the closed unit ball
added 204 characters in body
Mar
9
asked Multivariate ML inequality and holomorphic functions on the closed unit ball
Dec
12
awarded  Yearling