Question

Is sigma factor a transcription factor?
After I googled 'sigma TF' I stumbled upon two papers(only).
From a paper:
Sigma factors (sigmas) are bacterial transcription factors that bind core RNA polymerase (RNAP) and direct transcription initiation at cognate promoter sites.
and another paper had the title -
Specific binding of the transcription factor sigma-54 to promoter DNA.
However this contradicts with my book- Principle of Genetics Snustard and Simmons:
'Unlike their prokaryotic counterparts, eukaryotic RNAPs cannot initiate transcription by themselves ....require the assistance of protein transcription factors to start synthesis.'
What's your opinion?