  This paper expands further on a category theoretical formulation of
Hochschild cohomology for monoid objects in monoidal categories enriched over
abelian groups, which has been studied in arXiv:1605.00842. This topic was also
presented at ISCRA, Isfahan, Iran, April 2019. The present paper aims to
provide a more intuitive formulation of the Hochschild cochain complex and
extend the definition to Hochschild cohomology with values in a bimodule
object. In addition, an equivalent formulation of the Hochschild cochain
complex in terms of a cosimplicial object in the category of abelian groups is
provided.
