Tangle category
= Tangle category
Objects are finite words of strand orientations. Morphisms are boundary-fixed ambient-isotopy classes of oriented <tangles> in a slab, composed by stacking compatible boundary words; horizontal juxtaposition is the <tensor product>. Cups, caps, identity strands and crossings generate the category. Ordinary unframed isotopy includes all three <Reidemeister moves>; framed variants impose different first-move relations.