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1. • CommentRowNumber1.
   • CommentAuthorDean
   • CommentTimeSep 3rd 2020
   • PermaLink
   Author: Dean
   Format: MarkdownItexFibrations arise from the adjunction between context extension and dependent sum. They can also be defined by a certain lifting property, which coincides with identity type. I was wondering if there is a similar setup for cofibrations in a type theoretic paradigm. They are Eckmann Hilton dual, so I tried thinking about how to dualize the adjunctions that give rise to a fibration, but I didn't get anywhere. However, a certain extension property seems related (I can't quite tell what it should be), the one you get from dualizing the path space object construction. Does anyone know if there is a certain "co-context extension" and "codependent sum" which would give rise to cofibrations? Or really any setup.

   Fibrations arise from the adjunction between context extension and dependent sum. They can also be defined by a certain lifting property, which coincides with identity type.

   I was wondering if there is a similar setup for cofibrations in a type theoretic paradigm. They are Eckmann Hilton dual, so I tried thinking about how to dualize the adjunctions that give rise to a fibration, but I didn’t get anywhere. However, a certain extension property seems related (I can’t quite tell what it should be), the one you get from dualizing the path space object construction.

   Does anyone know if there is a certain “co-context extension” and “codependent sum” which would give rise to cofibrations? Or really any setup.