This paper has a double aim. First, in a historical and theoretical part, it shows how Ajdukiewicz's categorial grammar (1935) is directly related to Lesniewski's theory of semantic categories (1922). Secondly, it emphasizes that Ajdukiewicz's analysis of quantification constitutes a very anticipation of the contemporary categorial solutions which make use of lambda abstraction in order to deal with quantified expressions. In the absence of any published writting concerning the theory of semantic categories, the main categorial features of Lesniewski's languages are identified in analysing the two logical systems (Protothetics and Ontology) governed by the theory of semantic categories. This study points out the theoretical ideas which will be retained by later categorial grammars and which strongly contrast with Chomsky's transformational model. Furthermore, this analysis reminds that quantifiers were not categorized in Lesniewski's systems and explains this lack's reasons. After a short presentation of Ajdukiewicz's seminal categorial grammar, the paper exeamines Ajdukiewicz's treatment of quantification and shows how it constitutes an extension of Lesniewski's theory which foreshadows current compositional solutions.