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Dec
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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
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Does a left Kan lift of a homset functor Hom(*, - ): C -> {Set} through the forgetful functor {M-Set} -> {Set} exist?
Dec
19
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Socratic
Dec
18
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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
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Determining finite abelian groups among algebraic theories by counting
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12
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Yearling
Nov
9
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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.
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Mar
9
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Multivariate ML inequality and holomorphic functions on the closed unit ball
added 204 characters in body
Mar
9
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Multivariate ML inequality and holomorphic functions on the closed unit ball
added 204 characters in body
Mar
9
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Multivariate ML inequality and holomorphic functions on the closed unit ball
Dec
12
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Yearling
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