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  1. \makeatletter
  2. \newcommand{\xRightarrow}[2][]{\ext@arrow 0359\Rightarrowfill@{#1}{#2}}
  3. \makeatother
  4.  
  5. % Commands are often bracketed in {} to ensure they can be used sensible in sub/superscripts without explicit bracketing.
  6.  
  7. \newcommand{\cat}{\mathbf}
  8. \newcommand{\defeq}{\stackrel{\textup{def}}{=}}
  9. \newcommand{\set}{\cat{Set}}
  10. \newcommand{\Cat}{\cat{Cat}}
  11. \newcommand{\finset}{\mathbb{F}}
  12. \newcommand{\permset}{\mathbb{P}}
  13. \newcommand{\comp}{\circ}
  14. \newcommand{\op}{^{\textup{op}}}
  15. \newcommand{\too}{\longrightarrow}
  16. \newcommand{\psh}{\widehat}
  17. \newcommand{\Psh}[1]{\textup{Psh}(#1)}
  18. \newcommand{\CoPsh}[1]{\textup{CoPsh}(#1)}
  19. \newcommand{\pshF}{\psh{\finset}}
  20. \newcommand{\adj}{\dashv}
  21. \newcommand{\tuple}[1]{\langle#1\rangle}
  22. \newcommand{\unit}{\tuple{}}
  23. % Functor category
  24. \newcommand{\fcat}[2]{[#1, #2]}
  25. \newcommand{\inv}{^{-1}}
  26. \newcommand{\id}[1]{\textup{id}_{#1}}
  27. \newcommand{\Id}[1]{\textup{Id}_{#1}}
  28. \newcommand{\alg}[1]{\cat{#1\textup{-}alg}}
  29. \newcommand{\mon}[1]{\cat{#1\textup{-}mon}}
  30. \newcommand{\ev}{\textup{ev}_}
  31. \newcommand{\Lan}[2]{\textup{Lan}_{#1}(#2)}
  32. \newcommand{\Ran}[2]{\textup{Ran}_{#1}(#2)}
  33. \newcommand{\coend}[1]{\int^{#1}}
  34. \newcommand{\natto}{\Rightarrow}
  35. \newcommand{\xnatto}{\xRightarrow}
  36. \newcommand{\natiso}{\xnatto{\cong}}
  37. \newcommand{\codom}[1]{\textup{codom}(#1)}
  38. \newcommand{\denote}[1]{{\llbracket #1 \rrbracket}}
  39.  
  40. \newcommand{\cata}{\mathscr{A}}
  41. \newcommand{\catb}{\mathscr{B}}
  42. \newcommand{\catc}{\mathscr{C}}
  43. \newcommand{\catv}{\mathscr{V}}
  44. \newcommand{\ct}{\mathscr}
  45.  
  46. \newcommand{\smcat}{\mathbb}
  47. \newcommand{\smcata}{\mathbb{A}}
  48. \newcommand{\smcatb}{\mathbb{B}}
  49.  
  50. \newcommand{\nateq}{\simeq}
  51. \newcommand{\injto}{\hookrightarrow}
  52. \newcommand{\xto}{\xrightarrow}
  53. \newcommand{\xfrom}{\xleftarrow}
  54. \newcommand{\dom}{\textup{dom}}
  55. \newcommand{\yonem}{\mathbf{y}}
  56. \newcommand{\nat}{\mathbb{N}}
  57. \newcommand{\Hom}{\textup{Hom}}
  58. \newcommand{\st}{\enskip\vert\enskip}
  59. \newcommand{\disc}[1]{\textup{disc}(#1)}
  60. \newcommand{\el}[1]{\textup{el}(#1)}
  61. \newcommand{\const}{\underline}
  62.  
  63. \newcommand{\dsum}[1]{{\Sigma_{#1}}}
  64. \newcommand{\pb}[1]{{#1^{*}}}
  65. \newcommand{\dprod}[1]{{\Pi_{#1}}}
  66. \newcommand{\precomp}[1]{{#1^{\star}}}
  67. \newcommand{\kleene}{^{\star}}
  68.  
  69. % Typing rule
  70. \newcommand{\tr}[2]{\trc{\Gamma}{#1}{#2}}
  71. % Typing rule in extended context
  72. \newcommand{\trec}[3]{\trc{\Gamma, #1}{#2}{#3}}
  73. % Term with type
  74. \newcommand{\twt}[2]{#1 : #2}
  75. % Typing rule in context
  76. \newcommand{\trc}[3]{#1 \vdash \twt{#2}{#3}}
  77. % Typing rule in type context
  78. \newcommand{\trtc}[3]{#1 \rhd \twt{#2}{#3}}
  79.  
  80. \let\equiv\jeq
  81. \newcommand{\equiv}{\cong}
  82. \let\vec\smvec
  83. \newcommand{\vec}{\overrightarrow}
  84.  
  85. \newcommand{\ssth}{\textsuperscript{th}}
  86.  
  87. % KaTeX support
  88. \newcommand{\llbracket}{[\![}
  89. \newcommand{\rrbracket}{]\!]}
  90. \newcommand{\textup}{\mathrm}
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