# nLab reflective product-preserving sub-(∞,1)-category - internal formulation

Contents

### Context

#### $(\infty,1)$-topos theory

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

# Contents

## Idea

The external definition of reflective sub-(∞,1)-category via the universal property of the reflector has an immediate formulation in the internal language of an (∞,1)-topos. This internal formulation, however, automatically gives a reflective product-preserving sub-(∞,1)-category.

## References

HoTT-Coq code for internal reflective subcategories is at

The fact that in the internal formulation reflective subcategories are automatically product-preserving is mentioned on p. 5 of

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