Snippets: the Dominicans had been founded to purify the faith and fight “heresy”; from about 1250 on inquisitors were drafted from their ranks, and then also from the jesuits.
During the time of this story there existed a few small republics, and city states in (northern) Italy. A few united in a League. The papacy tried to gain influence, establish more Papal States - hence the quarrel about Imola, mentioned earlier in this story.
Since these states were mostly small, they relied on mercenaries for their infighting and defence. Read up on Federico Montefeltro in this connection here.
The yet unborn, illegitimate son of Giuliano de Medici (Giulio) will eventually become pope Clemens VII. Arguably one of the most challenging papal reigns…
The church of course never fought fair; Sixtus encouraged the Pazzi plot, his own relatives engaged in it. But when things turn sour it wasn’t a matter of a political, a power dispute, but was transcended into the realm of religious parlance. Sin, heresy, blasphemy, and such was the wielded as a powerful cudgel - one that left no viable response in earthly terms. It was less than 50 years later that Luther protested this church. And a century till Henry VIII split from Rome, because he was done with the church meddling in worldly matters, politics…