Deltas of Hochschild dimension one
Deltas of Hochschild dimension one
A theorem of Mitchell says that free categories have Hochschild dimension <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="less-than-or-slanted-equals 1"> <mml:semantics> <mml:mrow> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\leqslant 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The converse is shown to be true for all deltas (i.e. small skeletal categories whose only endomorphisms are the identities).