Garlef Wegart
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7h |
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objects which can’t be defined without making choices but which end up independent of the choice In representation theory one can often get the multiplicities as dimensions of $\mathrm{hom}(L,X)$ - $L$ being simple. Is there an analogous description for finite groups? |
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7h |
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objects which can’t be defined without making choices but which end up independent of the choice "This can only be done by listing properties of the object that characterise it up to some notion of equivalence." <-- I realised this to be not true - example: The fundamental group. Then again; in all the cases I can think of there is also a description via universal properties. Maybe this can be turned into an actual theorem? |
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1d |
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objects which can’t be defined without making choices but which end up independent of the choice Yes ~ the talk i linked does not deal with numerical computations but rather with type theoretic ones: contructive proofs. And it seems we are looking for a constructive proof of the existence of square roots using the description of the reals via cauchy sequences - without choosing representatives. Which seens to be the same question as asking if infima can be described without chosing represenatives. |
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1d |
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objects which can’t be defined without making choices but which end up independent of the choice Again; the distinction is between characterisation and implemention. Characterising the square root is trivial (it's the unique real number that results in the original number, when squared). Implementing it using the description of the reals i gave above is pretty easy. Implementing it for the implementation of the reals via cauchy sequences seems to be nontrivial ~ at least to me :D. There is a series of videolectures concerning questions like this, if i remember correctly: videolectures.net/aug09_spitters_oconnor_cvia |
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1d |
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objects which can’t be defined without making choices but which end up independent of the choice Toink is right - to state it differently: The set of Cauchy sequences inherits the addition from $\mathbb Q$. The addition is compatible with the equivalence relation at hand and thus carries over to the quotient $\mathbb R$. |
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objects which can’t be defined without making choices but which end up independent of the choice added 1 characters in body |
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objects which can’t be defined without making choices but which end up independent of the choice added 312 characters in body; added 4 characters in body; added 4 characters in body |
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objects which can’t be defined without making choices but which end up independent of the choice added 62 characters in body; deleted 109 characters in body; added 74 characters in body |
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answered | objects which can’t be defined without making choices but which end up independent of the choice |
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Apr 23 |
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Composition of Cat-valued distributors - compatible with grothendieck construction? added 158 characters in body |
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Apr 23 |
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Composition of Cat-valued distributors - compatible with grothendieck construction? Yeah; It seems i was a bit vauge. I reformulated the question to make it more comprehensible. |
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Apr 23 |
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Composition of Cat-valued distributors - compatible with grothendieck construction? Reformulated the question.; deleted 35 characters in body |
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Apr 22 |
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grothendieck construction for profunctors Thanks for the refrerence. This seems to be the characterisation i was looking for; let's see if this helps with my other question. :) |
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Apr 22 |
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grothendieck construction for profunctors changed lax to oplax |
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Apr 22 |
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grothendieck construction for profunctors added 158 characters in body |
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Apr 22 |
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Composition of Cat-valued distributors - compatible with grothendieck construction? added 61 characters in body |
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Apr 22 |
asked | grothendieck construction for profunctors |
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Apr 22 |
asked | Composition of Cat-valued distributors - compatible with grothendieck construction? |
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Apr 22 |
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(Co-)Limits and fibrations of DG-Categories? Hm... wether it is the lax- or oplax-colimit depends on how you define the grothendieck construction: you chose the vertical part of a morphism to be either $f_*x\to x'$ or $x' \to f_*x$; both work equally and we have $\int'_C F = \int_C op \circ F$ |
