NOVELTY - Co-processing biomass feedstock and refinery feedstock in a refinery unit comprises producing liquid product by catalytically cracking a biomass feedstock and a refinery feedstock in a refinery unit comprising fluidized reactor, where catalytically cracking comprises transferring hydrogen from the refinery feedstock to carbon and oxygen from the biomass feedstock.    USE - The method is for co-processing biomass feedstock and refinery feedstock in a refinery unit (claimed). It is used for producing fuel including light gases (e.g. ethane, propane, and butane), naphtha, and distillates (e.g. jet fuel, diesel, and heating oil); specialty chemical including light olefins (e.g. ethylene, propylene, and butylenes), acids (e.g. formic and acetic acids), aldehydes, alcohols (e.g. ethanol, propanol, butanol, or phenols), ketones, and furans; and/or intermediate product from biomass.    ADVANTAGE - The method is conducted under conditions that can mitigate equipment cost, energy cost, and/or degradation or undesirable reaction of conversion product. It can adapt existing refinery processes for co-processing biomass feedstock (e.g. change operating parameters, catalyst, and feedstock), retrofit existing refinery process units for processing biomass (e.g. adding an extra riser for biomass catalytic cracking or adding solid biomass feeder system to introduce biomass), and construct new, purpose-built biomass reactors (e.g. employ commercially available conventional reactor components). Thus, the method can reduce the cost and increase the availability of fuel and/or specialty chemicals derived from biomass. The method provides processing under mild conditions and product selectivity. It results in higher yield and higher value products being produced from both the biomass and refinery feedstock. By co-processing, the biomass feedstock produces hydrogen products that are richer in hydrogen and contain less undesired oxygenic and acidic groups, and fewer undesired aromatic compounds. By co-processing, the refinery feedstock produces higher octane products (e.g. with more olefins) having less pour point problems. Co-processing can have the synergistic effect of simultaneously increasing the commercial value and utility of product streams from both feedstocks.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for:    (1) co-processing biomass feedstock and refinery feedstock in the presence of hydrogen gas in a refinery unit comprising producing liquid product by hydrocracking or hydrotreating a biomass feedstock and refinery feedstock in the presence of hydrogen gas in a refinery unit comprising hydrocracking or hydrotreating reactor, where hydrocracking or hydrotreating comprises transferring hydrogen from the hydrogen gas to carbon and oxygen from the biomass feedstock and to carbon from the refinery feedstock;    (2) a refinery unit for co-processing biomass feedstock and refinery feedstock comprising fluidized reactor; first system providing biomass feedstock and refinery feedstock to the fluidized reactor; and a second system for refreshing and/or regenerating catalyst for the fluidized reactor, where first and second systems support catalytic cracking;    (3) a method for providing refinery unit for co-processing biomass feedstock and refinery feedstock comprising providing fluidized reactor; providing first system, which provides biomass feedstock and refinery feedstock to the fluidized reactor; and providing a second system for refreshing and/or regenerating catalyst in the fluidized reactor;    (4) refinery unit for co-processing biomass feedstock and refinery feedstock in the presence of hydrogen gas comprising hydrocracking or hydrotreating reactor; first system providing biomass feedstock, refinery feedstock, and hydrogen gas to the hydrocracking or hydrotreating reactor; and a second system for refreshing and/or regenerating catalyst in the hydrocracking or hydrotreating reactor, where first and second systems support hydrocracking or hydrotreating comprising transferring hydrogen from the hydrogen gas to carbon and oxygen from the biomass feedstock and to carbon from the refinery feedstock in the hydrocracking or hydrotreating reactor; and    (5) a method for providing refinery unit for co-processing biomass feedstock and refinery feedstock in the presence of hydrogen gas comprising providing hydrocracking or hydrotreating reactor; providing a first system providing biomass feedstock, refinery feedstock, and hydrogen gas to the hydrocracking or hydrotreating reactor; and providing a second system for refreshing and/or regenerating catalyst in the hydrocracking or hydrotreating reactor.