# Lie theory of multiplicative tensors

## TL;DR

This paper characterizes multiplicative tensors on Lie groupoids using infinitesimal data, unifying various structures like forms, multivectors, and holomorphic structures, and provides a comprehensive treatment of vector-valued forms and Nijenhuis operators.

## Contribution

It offers a complete infinitesimal description of multiplicative tensors on Lie groupoids, unifying multiple geometric structures under a common framework.

## Key findings

- Complete infinitesimal description of multiplicative tensors
- Unified treatment of forms, multivectors, and holomorphic structures
- Analysis of multiplicative vector-valued forms and Nijenhuis operators

## Abstract

We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the infinitesimal counterparts of multiplicative forms, multivector fields and holomorphic structures, obtained through a unifying and conceptual method. We also give a full treatment of multiplicative vector-valued forms, particularly Nijenhuis operators and related structures.