Abstract
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 To each oriented surface 
,
 we associate a differential graded category
 
. The homotopy
 category 
 is a triangulated category which satisfies properties akin to those of the contact
 categories studied by K Honda. These categories are also related to the algebraic
 contact categories of Y Tian and to the bordered sutured categories of R
 Zarev.
  
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              Keywords
              
                contact geometry, Heegaard–Floer, topological quantum field
                theory
               
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              Mathematical Subject Classification 2010
              
                Primary: 53D10
               
              
                Secondary: 18G55
               
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              Publication
              
                Received: 20 July 2017
               
              
                Revised: 3 April 2023
               
              
                Accepted: 25 April 2023
               
              
                Published: 19 August 2024
               
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