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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 4th 2014
   • (edited Feb 4th 2014)
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   Author: Urs
   Format: MarkdownItexI'd be trying to write out a more detailed exposition of how fiber integration in twisted generalized cohomology/twisted Umkehr maps are axiomaized in linear homotopy-type theory. To start with I produced a dictionary table, for inclusion in relevant entries: * _[[twisted generalized cohomology in linear homotopy type theory -- table]]_

   I’d be trying to write out a more detailed exposition of how fiber integration in twisted generalized cohomology/twisted Umkehr maps are axiomaized in linear homotopy-type theory.

   To start with I produced a dictionary table, for inclusion in relevant entries:

   • twisted generalized cohomology in linear homotopy type theory – table
2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 27th 2023
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   Author: David_Corfield
   Format: MarkdownItexWhy the same final entry in these two rows? | [[dependent sum]] | [[generalized homology]] [[spectrum]] | [[space of quantum states]] ("[[bra-ket|bra]]") | | [[dual type|dual]] of [[dependent sum]] | [[generalized cohomology]] [[spectrum]] | [[space of quantum states]] ("[[bra-ket|ket]]") | Elsewhere homology is related to observables.

   Why the same final entry in these two rows?

   | dependent sum | generalized homology spectrum | space of quantum states (“bra”) |

   | dual of dependent sum | generalized cohomology spectrum | space of quantum states (“ket”) |

   Elsewhere homology is related to observables.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 27th 2023
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   Author: Urs
   Format: MarkdownItexThose "bra"-s, being "dual pure states" $\langle \psi \vert \,\colon\, \mathcal{H} \to \mathbb{C}$ are a kind of observable, namely reflecting the observation: "system is in state $\psi$". But without monoid structure on the base space (such as it being a loop space) there is no algebra structure induced on its homology, and hence no canonical structure of an "algebra of observables".

   Those “bra”-s, being “dual pure states” $\langle \psi \vert \,\colon\, \mathcal{H} \to \mathbb{C}$ are a kind of observable, namely reflecting the observation: “system is in state $\psi$”.

   But without monoid structure on the base space (such as it being a loop space) there is no algebra structure induced on its homology, and hence no canonical structure of an “algebra of observables”.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 27th 2023
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   Author: David_Corfield
   Format: MarkdownItexAh, Ok. Thanks!

   Ah, Ok. Thanks!