# Category of mixed plectic Hodge structures

## TL;DR

This paper explores the properties of the category of mixed plectic Hodge structures, providing an equivalent description via filtrations and constructing a complex to compute extension groups, advancing understanding in Hodge theory.

## Contribution

It offers an alternative description of mixed plectic Hodge structures and explicitly constructs a complex for calculating extension groups, enhancing computational tools.

## Key findings

- Equivalent description via weight and partial Hodge filtrations
- Construction of an explicit complex for extension groups
- Deeper understanding of the structure of mixed plectic Hodge categories

## Abstract

The purpose of this article is to investigate the properties of the category of mixed plectic Hodge structures defined by Nekov\'a\v{r} and Scholl. We give an equivalent description of mixed plectic Hodge structures in terms of the weight and partial Hodge filtrations. We also construct an explicit complex calculating the extension groups in this category.