CHRISTIAN MARCEL DE AMORIM PERRET GENTIL DIT MAILLARD

Category theory is a mathematical logic language first developed in the early 1940s. It was in fact worked on by logicians, bringing results to the field from the 1950s and 1960s onwards. The work on constructing of a categorical semantics for first-order languages was possible from the construction of a new category, called elementary topos, which led to relevant results from a philosophical point of view, such as that the underlying logic of a topos is intuitionistic logic. A new category, called prototopos, simpler than the elementary topos category, in which it is possible to derive a semantics for the propositional calculus, will be presented, making an exhaustive comparison with the elementary topos category and the quasitopos category.