JohnBurke

Fractional operators don't have OpSpecs. They have M-specs (Management Specifications, as opposed to Operations Specifications). M-Specs are required under 14 CFR 91.1015: https://www.ecfr.gov/current/title-14/section-91.1015

M-Specs are to fractional management operations what OpSpecs are to air carrier operations and repair stations (14 CFR parts 121, 125, 135, 145). Both are Special Authorizations, a broad term which cover Letters of Autorization (LOA's), Letters of Deviation Authority (LODA's), Operations Specifications (OpSpecs), and Management Specifications (MSpecs).

You can find the breakdown of all things Special Authorizations by going to the Document Regulatory System (DRS), FAA Order 8900.1 (Flight Standards Information Mangement System, Change 872)), Volume 3, Chapter 18, sections 3 through 6.

https://drs.faa.gov/browse/excelExte...125163342.0001
https://drs.faa.gov/browse/excelExte...010153932.0001
https://drs.faa.gov/browse/excelExte...101185520.0001
https://drs.faa.gov/browse/excelExte...219160545.0001

OpSpec C056/C057, issued to certificate holders (121, 125, 135) is not issued to MSpec holders (91K). C056 and C057 cover lower-than-standard takeoff minimums.

Standard takeoff minimums are spelled out in 91.175(f): https://www.ecfr.gov/current/title-14/section-91.175

Specific to your question about OpSpec/MSpec, 8900.1, Volume 3, Chapter 18, Section 5 is applicable, as linked above: https://drs.faa.gov/browse/excelExte...101185520.0001

Look at C056/C057, and C078/C079. Neither C056, nor C057 is available to Part 91K fractional MSpecs. C078 is applicable to 121 and 125 operators, and C079 to 135 operators. Keep in mind that 91K oeprators can also hold certification under 135 and do 135 flights, with the applicable special authorization of Opspecs C057 and C079, if issued.

91K operators require a takeoff alternate under 91.1039(d), when visibility is above takeoff minimums, but less than landing minimums. 91.1039(e), as noted previously, requires compliance with applicable IFR takeoff weather minums, the two allowable exceptions specified for enhanced vision operators in their MSpec, and 91.175(f); standard minmums, but must also observe applicable Part 97 (instrument takeoff minimums) limitations (linked above).