5 papers
Lax Distributivity and a Characterization of Abelian Categories
Martin Markl, Dominik Trnka
We show that abelian categories can be characterized as structures consisting of a colax algebra and a lax algebra connected by a lax mixed rewriting rule. To this end we develop a…
Kernels, lax algebras, décalage, and supercoherence
Martin Markl, Dominik Trnka
We prove that a pointed category has kernels if and only if it is a lax algebra for the arrow 2-monad, and that this holds if and only if it is the décalage of a supercoherent stru…
Integration of a categorical operad
Dominik Trnka
We describe a Grothendieck construction for non-symmetric operads with values in categories, and hence in groupoids and posets. The construction produces a 2-category which is oper…
Operadic Fibrations and Unary Operadic 2-categories
Dominik Trnka
We introduce unary operadic 2-categories as a framework for operadic Grothendieck construction of a categorical O-operad, O being a unary operadic category. The construction is a f…
Category-colored Operads, Internal Operads, and Markl -operads
Dominik Trnka
We present a Markl-style definition of operads colored by a small category. In the presence of a unit these are equivalent to substitudes of Day and Street. We show that operads co…