Past studies have shown that pigeons can learn complex categories and can also remember large numbers of individual objects. In recent work, Cook et al. Psychonomic Bulletin & Review, 28, 548-555, (2021) provided evidence that pigeons may use a dynamic combination of both category-based information and item-specific memorization to solve a categorical variation of the mid-session reversal (MSR) task, which is an influential task for exploring the nature of temporally organized behaviors in animals. To provide greater insight into these pigeons' behaviors, in this article we developed and investigated different computational models and their variations to account for these data. Of these, two models emerged as good candidates. One was a multinomial-processing-tree categorization/memory model, formalizing the two-process mechanism initially proposed by Cook et al. Psychonomic Bulletin & Review, 28, 548-555, (2021). The second was a new object/time-coding model, which posits the storage of object-specific memories with an additional within-session time code and assumes that a basic stimulus generalization process underlies the pigeons' choice behavior. Both provided high-quality fits to the published sets of training and transfer data collected in the categorical MSR task. These computational efforts give deeper insights into the theoretical mechanisms underlying the temporal and sequential structure of behavior in animals and stimulate future empirical research further revealing the organization of the pigeons' cognitive processes.