Skip to main content

Category Theory & Homological Algebra

Seminar notes for a fictional pure-mathematics institute, from a single declarative JSON source. The notation leans hard on arrows, scripts and fraktur — a stress test for the math engine's symbol coverage.

  • Categories and functors. A functor F: mathcal{C} ⟶ mathcal{D} preserving composition g circ f and identities, with hom-sets mathrm{Hom}_{mathcal{C}}(A, B).
  • Natural transformations. eta: F ⟹ G and the naturality condition, plus adjunctions.
  • Short exact sequences. Monomorphisms and epimorphisms with hooked and two-headed arrows — 0 ⟶ A ↪ B ↠ C ⟶ 0.
  • Homological algebra. Chain complexes (partial_{n} circ partial_{n+1} = 0), homology H_{n} = ker partial_{n} / mathrm{im} partial_{n+1}, the long exact sequence, and the derived functors mathrm{Ext} and mathrm{Tor}.
  • Lie algebras in fraktur. mathfrak{g} with its bracket, mathfrak{su}(2) and mathfrak{sl}(n, CC), the Jacobi identity, and the Yoneda embedding.
  • Dressed as a publication. A drawn academic crest, a SPECIMEN watermark, a MicroQR verification mark, and a vertical EAN-13 ISSN spine mounted in the margin via a rotated canvas group.

Glyphs are positioned from the font's OpenType MATH table and written into the PDF as selectable, searchable text — never a flattened image. Latin Modern Math covers the fraktur, script and long-arrow notation here; the STIX coverage font stands behind it for anything it lacks.

Features used: Shortcodes, Tables, Columns, Canvas, Barcodes, Watermarks, Headers & Footers, Styles