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Formed at the cerebral cortex, neuron cell assemblies are regarded as basic units in cortical representation. Proposed by Hebb, these cell assemblies are regarded as the distributed neural representation of relevant objects, concepts or constellations. Each cell assembly contains a group of neurons having strong mutual excitatory connections. During a stimulus, these cells get activated. This activation either performs a given action or represent a given percept or concept in brain. This theory is in the strongest connection of the problem of concept forming in the brain. The challenge is to model coordinated activity among neurons in brain mathematically. The need of modelling it mathematically enables this paper to give clear view of functionality of Hebbian cell assembly. Therefore this paper proposes a pragmatic approach to Hebbian cell assemblies using mathematical model grounded in lattice based formalism that utilizes Galois connections. During this proposal, the authors also show the connections of the proposal to cognitive model of memory in particularly long-term memory (LTM).