Detail publikačního výsledku

INTEGRATION OF A CATEGORICAL OPERAD

Trnka Dominik, Mgr., Ph.D.

Originální název

INTEGRATION OF A CATEGORICAL OPERAD

Anglický název

INTEGRATION OF A CATEGORICAL OPERAD

Druh

Článek WoS

Originální abstrakt

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 operadically fibered over the category Δ_s of finite non-empty ordinals and surjections. We describe an inverse for the construction, yielding an equivalence of constant-free non-symmetric categorical operads and operadic 2-categories (split-)fibered over Δ_s, which resembles the correspondence of categorical presheaves and fibered categories. The result provides a new characterization of non-symmetric categorical operads and tools to study them.

Anglický abstrakt

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 operadically fibered over the category Δ_s of finite non-empty ordinals and surjections. We describe an inverse for the construction, yielding an equivalence of constant-free non-symmetric categorical operads and operadic 2-categories (split-)fibered over Δ_s, which resembles the correspondence of categorical presheaves and fibered categories. The result provides a new characterization of non-symmetric categorical operads and tools to study them.

Klíčová slova

Grothendieck construction; Categorical operad; Integration; Non-symmetric operad; 2-category; Operadic fibration

Klíčová slova v angličtině

Grothendieck construction; Categorical operad; Integration; Non-symmetric operad; 2-category; Operadic fibration

Autoři

Trnka Dominik, Mgr., Ph.D.

Rok RIV

2026

Vydáno

13.01.2026

Periodikum

Theory and Applications of Categories

Svazek

45

Číslo

3

Stát

Kanada

Strany od

130

Strany do

150

Strany počet

21

URL

http://www.tac.mta.ca/tac/volumes/45/3/45-03abs.html

BibTex

@article{BUT201697,
  author="Dominik {Trnka}",
  title="INTEGRATION OF A CATEGORICAL OPERAD",
  journal="Theory and Applications of Categories",
  year="2026",
  volume="45",
  number="3",
  pages="130--150",
  issn="1201-561X",
  url="http://www.tac.mta.ca/tac/volumes/45/3/45-03abs.html"
}