nLab coalgebroid

Idea:

Coalgebroid is a horizontal categorification of a coalgebra. The concept may be introduced in various levels of generality.

Literature:

• Phùng Hô Hai, Tannaka-Krein duality for Hopf algebroids, Israel Journal of Mathematics 167, 193–225 doi

• Paddy McCrudden, Categories of representations of coalgebroids, Adv. Math. 154:2 (2000) 299–332 doi

• Ramón Abud Alcalá, Oplax actions and enriched icons with applications to coalgebroids and quantum categories, PhD thesis, Macquarie Univ. 2017 repository

The commutative case is dual to an internal category in the category of affine schemes

• Yifei Zhao, Tannakian reconstruction of coalgebroids, In: Stacks Project Expository Collection (SPEC), London Math. Soc. Lec. Note Series 480, 268–289 doi

We explain a theorem of D. Schäppi on the reconstruction of an affine category scheme (dually, a coalgebroid) over a general commutative ring from its category of finite-rank representations.

category: algebra