<ul data-eligibleForWebStory="true">Decision-making tasks in cognition are commonly modeled using Drift Diffusion Models (DDMs) and Poisson counter model.These models lack a learning mechanism and are limited to tasks where participants have prior knowledge of the categories.A proposal for a Spiking Neural Network (SNN) model for decision-making is made to bridge the gap between cognitive and biological models.The SNN model incorporates a learning mechanism and neuron activities are modeled by a multivariate Hawkes process.A coupling result between DDM and the Poisson counter model is shown, indicating similar categorizations and reaction times.The DDM can be approximated by spiking Poisson neurons.A particular DDM with correlated noise can be derived from a Hawkes network of spiking neurons governed by a local learning rule.An online categorization task was designed to evaluate the model predictions.The work aims to integrate biologically relevant neural mechanisms into cognitive models for a deeper understanding of neural activity and behavior.